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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 09:50:28
Then I did, $0< \frac{2c}{c-5}<3$
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
510,789,298,321,096,700
TeXit
02/21/2022 09:50:30
**Sakata Yaksha**
https://cdn.discordapp.c…603087384657.png
748029603087384657.png
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 09:50:34
And took intersection, my answer however does not match to the correct one, did I miss something perhaps?
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 09:54:13
My final answer is $5<c<15$
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
510,789,298,321,096,700
TeXit
02/21/2022 09:54:16
**Sakata Yaksha**
https://cdn.discordapp.c…603087384657.png
748029603087384657.png
0
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:08:15
@Helpers
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:19:46
🥲
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
193,942,262,336,454,660
KurtDee
02/21/2022 10:35:48
What is an integral value
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
193,942,262,336,454,660
KurtDee
02/21/2022 10:35:51
A root?
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1
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:35:56
#❓how-to-get-help
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
193,942,262,336,454,660
KurtDee
02/21/2022 10:35:56
X=0?
0
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
193,942,262,336,454,660
KurtDee
02/21/2022 10:36:19
Okay I’ll go get help then 🙄
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1
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:36:20
Oh lol.
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:36:24
You're helping me
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:36:26
I forgot
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:36:35
I thought you were asking something of your own.
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:36:49
So integral value means a value which is integer.
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
193,942,262,336,454,660
KurtDee
02/21/2022 10:37:31
So integer values of c
0
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
193,942,262,336,454,660
KurtDee
02/21/2022 10:37:39
Okay
0
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:37:42
Yeah
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
193,942,262,336,454,660
KurtDee
02/21/2022 10:38:21
Have you tried solving quadratic equation and restraining there
0
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:38:39
Solving the quadratic equation, you mean using quadratic formula?
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
193,942,262,336,454,660
KurtDee
02/21/2022 10:38:45
Yeah that’s what I mean
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:38:49
That makes no sense does it?
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
193,942,262,336,454,660
KurtDee
02/21/2022 10:39:04
Your constraint is on the two roots, no?
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:39:14
Definitely.
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:39:21
But wouldn't that be crazy calculation?
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
193,942,262,336,454,660
KurtDee
02/21/2022 10:39:47
I mean like there’s only one way to find out
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help-10
6268617cabf8450aa15187f8b1e4eb88
193,942,262,336,454,660
KurtDee
02/21/2022 10:40:55
I personally would then break it into two restraints for the /pm
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help-10
6268617cabf8450aa15187f8b1e4eb88
193,942,262,336,454,660
KurtDee
02/21/2022 10:41:01
Try to bound them
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
193,942,262,336,454,660
KurtDee
02/21/2022 10:41:08
Get a range for c for each one
0
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
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Navix
02/21/2022 10:41:15
No it's not that hard
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:41:22
Well if the roots are between 0,2 and 2,3 the roots are basically in interval (0,3) therefore p(2) is negative. Then sum of the roots also lies in the interval (0,3)
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:41:28
I used stuff like This
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
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Navix
02/21/2022 10:41:28
the roots in terms of c will be an increasing function for the smaller root and a decreasing function for the bigger root
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:44:09
How would that be?
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 10:44:30
If you use the quadratic formula it simplifies quite nicely at the end, imo
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:44:44
I see, I'll try that then.
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:45:11
But then I'll have two roots. Which one do I put in first interval lol.
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:45:20
If that's how we're doing it.
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 10:45:42
the terms for the roots just differ by a minus sign
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help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 10:46:03
so the bigger root corresponds to the term with the positive sign
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:46:37
No.
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:46:48
That's not really correct imo.
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 10:47:05
write it out
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:47:05
p+q>p-q are you implying?
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:47:14
Okay yeah my bad XD.
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 10:48:29
No, if you apply the quadratic formula you'll get x_1 and x_2, the two roots in terms of c, only. x_1 = u(c) + v(c) and x_2 = u(c) - v(c). Something like that should come out
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 10:48:52
v(c) is a square root so that can only be positive
0
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 10:49:00
unless you deal with complex numbers
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:49:04
$\frac{2c±\sqrt{4c^2-4(c-5)(c-4)}}{2(c-5)}$
1
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799
help-10
6268617cabf8450aa15187f8b1e4eb88
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TeXit
02/21/2022 10:49:07
**Sakata Yaksha**
https://cdn.discordapp.c…603087384657.png
748029603087384657.png
0
1
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799
help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 10:51:44
I got $x_{1,2} = \frac{c}{c-5} \pm \sqrt{\qty(\frac{c}{c-5})^2 - \frac{c-4}{c-5}}$
0
1
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799
help-10
6268617cabf8450aa15187f8b1e4eb88
510,789,298,321,096,700
TeXit
02/21/2022 10:51:47
**Navix**
https://cdn.discordapp.c…051794391040.png
392341051794391040.png
0
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:54:12
It is.
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:54:37
Yes, now?
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 10:55:07
common denominator and simplify
0
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 10:58:23
should become $\frac{c \pm \sqrt{9c - 20}}{c-5}$
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799
help-10
6268617cabf8450aa15187f8b1e4eb88
510,789,298,321,096,700
TeXit
02/21/2022 10:58:26
**Navix**
https://cdn.discordapp.c…051794391040.png
392341051794391040.png
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392,341,051,794,391,040
Navix
0001
nvx
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799
help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:59:46
Alright, I'm back.
1
0
748,029,603,087,384,700
Yours truly
3785
What the hell am I doing here?
false
799
help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 10:59:50
So, this is correct.
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 11:00:32
Even then
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 11:00:41
There's no way to say the one with plus sign is larger root.
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 11:00:43
Obviously.
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 11:00:45
why not?
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1
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 11:00:57
Bruh.
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 11:01:21
well split into two cases: c > 5 and c < 5
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 11:02:09
Lol at c=3 check for yourself first of all.
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 11:02:18
Now you're talking.
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 11:03:31
But truly mate, this is too much work I'd say. I'll try it this way too definitely, could you find an error in my calculation and stuff too for reference? I'd appreciate it.
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
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Navix
02/21/2022 11:03:56
Yea, I'll work it out this way and show you if you want, as well
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help-10
6268617cabf8450aa15187f8b1e4eb88
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Yours truly
02/21/2022 11:04:14
Yes, so first we'll finish it this way.
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
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Yours truly
02/21/2022 11:04:43
For c>5 the denominator is always positive, and so is numerator.
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
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Yours truly
02/21/2022 11:05:16
C≥20/9
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
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Yours truly
02/21/2022 11:05:29
This we have to always keep in mind as well.
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
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Yours truly
02/21/2022 11:06:09
So case the two cases would be c>5 second 29/5≤c<5
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 11:06:17
But cases for what?
1
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 11:06:43
It's not like we have any RHS.
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
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Navix
02/21/2022 11:07:00
What I did was notice that the term is an increasing function on c > 5.
0
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help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 11:07:25
So we should be able to simply set it equal to the endpoints?
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6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 11:07:39
of the root boundaries
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392,341,051,794,391,040
Navix
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6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 11:07:56
Basically the minimum value for the function should lie in interval (2,3)?
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help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 11:09:11
That's what I thought
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help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 11:11:08
basically for c > 5 the smaller root in (0,2) will be the term with the minus sign. so to find the bounds for c we can simply set this term equal to 2 and 0 and solve for c.
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help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 11:12:36
because it's increasing, that should also correspond to the interval for our feasible values for c
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null
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help-10
6268617cabf8450aa15187f8b1e4eb88
551,807,466,631,987,200
Mat
02/21/2022 11:14:01
A quick solution comes from just setting $$p(0)p(3)>0 \land p(0)p(2)<0,$$ which gives $13 \leq c \leq 23$
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help-10
6268617cabf8450aa15187f8b1e4eb88
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TeXit
02/21/2022 11:14:18
**Mat**
https://cdn.discordapp.c…466631987211.png
551807466631987211.png
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 11:17:47
That's what I was talking about.
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 11:18:03
I did p(2) part, but not p(0)p(3) thingy.
1
0
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799
help-10
6268617cabf8450aa15187f8b1e4eb88
392,341,051,794,391,040
Navix
02/21/2022 11:18:11
Agree, that's pretty neat
0
1
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799
help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 11:18:36
Yes, this is the only way I do these, unfortunately my sol was lacking as you can see.
1
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 11:18:41
That was nice, thanks mate.
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help-10
6268617cabf8450aa15187f8b1e4eb88
748,029,603,087,384,700
Yours truly
02/21/2022 11:20:52
.close
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0
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help-10
8389a9cf55bd4018b4523970c9f858a3
748,029,603,087,384,700
Yours truly
02/21/2022 11:21:01
.reopen
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help-10
8389a9cf55bd4018b4523970c9f858a3
551,807,466,631,987,200
Mat
02/21/2022 11:21:15
Np! Yeah we were basically on the same idea
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help-10
8389a9cf55bd4018b4523970c9f858a3
748,029,603,087,384,700
Yours truly
02/21/2022 11:21:27
Hm, yeah.
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help-10
8389a9cf55bd4018b4523970c9f858a3
748,029,603,087,384,700
Yours truly
02/21/2022 11:21:28
.close
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aeb6e91318fb4adfa044352ee7763f86
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Deleted User
02/21/2022 11:37:03
https://cdn.discordapp.c…20221_220551.jpg
IMG_20220221_220551.jpg
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help-10
aeb6e91318fb4adfa044352ee7763f86
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Deleted User
02/21/2022 11:37:03
Find if convergent or divergent
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0
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help-10
aeb6e91318fb4adfa044352ee7763f86
332,849,454,753,251,300
sucka mah
02/21/2022 11:37:47
use the integral test. Take the integral of that series and see if the value of the integral is fixed or if it goes towards infinity.
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1
551,807,466,631,987,200
Mat
9616
Mat
false