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2 classes
343
help-10
cb6d002ea2f245b89e983001acb3f6a9
456,226,577,798,135,800
Deleted User
01/28/2022 12:01:50
thats what i remember
1
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help-10
cb6d002ea2f245b89e983001acb3f6a9
334,482,942,506,041,340
Zybikron
01/28/2022 12:02:28
ah, yeah that sounds right
0
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help-10
cb6d002ea2f245b89e983001acb3f6a9
456,226,577,798,135,800
Deleted User
01/28/2022 12:02:30
i want to get like a proper derivation of these kinds of sums, instead of proving them by using proof by induction
1
0
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help-10
cb6d002ea2f245b89e983001acb3f6a9
456,226,577,798,135,800
Deleted User
01/28/2022 12:03:10
ohh yeah fine then seems like i can take care, thanks for the help!
1
0
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help-10
cb6d002ea2f245b89e983001acb3f6a9
456,226,577,798,135,800
Deleted User
01/28/2022 12:03:28
.close
1
0
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help-10
a42d564cde584a1684bb0e7de451fe7b
755,831,671,588,126,700
RepliedPencil
01/28/2022 12:10:17
What is the difference between a class and a set?
1
0
null
null
null
null
null
344
help-10
a42d564cde584a1684bb0e7de451fe7b
334,482,942,506,041,340
Zybikron
01/28/2022 12:15:27
A class is a set with some criteria. A set is a set.
0
1
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help-10
a42d564cde584a1684bb0e7de451fe7b
334,482,942,506,041,340
Zybikron
01/28/2022 12:16:32
they're used pretty synonymously since most of the time you'll probably want some criteria on your set
0
1
null
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null
null
344
help-10
a42d564cde584a1684bb0e7de451fe7b
356,908,116,429,897,700
Kaynex
01/28/2022 12:17:53
Some objects can't be made into sets. This is made clear by a few paradoxes in set theory.
0
1
334,482,942,506,041,340
Zybikron
5611
Zybikron
false
344
help-10
a42d564cde584a1684bb0e7de451fe7b
356,908,116,429,897,700
Kaynex
01/28/2022 12:18:06
Classes are our attempt to build collections that don't need to also be sets
0
1
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help-10
a42d564cde584a1684bb0e7de451fe7b
356,908,116,429,897,700
Kaynex
01/28/2022 12:18:37
One of the most important things about classes is that they need not be sets, but are still collections of stuff.
0
1
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help-10
a42d564cde584a1684bb0e7de451fe7b
334,482,942,506,041,340
Zybikron
01/28/2022 12:20:21
isn't a set, at it's most basic definition, a collection of stuff?
0
1
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help-10
a42d564cde584a1684bb0e7de451fe7b
356,908,116,429,897,700
Kaynex
01/28/2022 12:20:29
Ye
0
1
null
null
null
null
null
344
help-10
a42d564cde584a1684bb0e7de451fe7b
356,908,116,429,897,700
Kaynex
01/28/2022 12:21:23
Well, no. A set, at its most basic definition, is any object that obeys the rules in ZFC.
0
1
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help-10
a42d564cde584a1684bb0e7de451fe7b
334,482,942,506,041,340
Zybikron
01/28/2022 12:21:46
Right, it's a collection of stuff that doesn't create a paradox
0
1
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help-10
a42d564cde584a1684bb0e7de451fe7b
334,482,942,506,041,340
Zybikron
01/28/2022 12:22:03
but your last line basically says "A class doesn't need to be a set, but it's a set"
0
1
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help-10
a42d564cde584a1684bb0e7de451fe7b
755,831,671,588,126,700
RepliedPencil
01/28/2022 12:27:29
Ohh alright thanks everyone!!
1
0
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null
345
help-10
de8c8807f5e141cfa82c416d0506b750
293,744,814,472,822,800
Bunnies_
01/28/2022 12:38:42
since alpha and beta are roots, can you think of a way to write f(x) in terms of alpha and beta?
1
0
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help-10
de8c8807f5e141cfa82c416d0506b750
293,744,814,472,822,800
Bunnies_
01/28/2022 12:40:09
Hint: || f(x) = (x-alpha)(x-beta)||
1
0
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345
help-10
de8c8807f5e141cfa82c416d0506b750
261,933,205,387,477,000
riemann
01/28/2022 12:49:21
do you know the quadratic formula?
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
261,933,205,387,477,000
riemann
01/28/2022 12:50:05
you should understand why
0
1
null
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 12:55:38
Given f(x) has only two real distinct roots $\alpha, \, \beta$, do you know a way to write the polynomial f(x)?
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
510,789,298,321,096,700
TeXit
01/28/2022 12:55:41
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 12:56:53
Okay, then... Do you know what does it mean for a polynomial to have a root?
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 12:57:03
what is it?
0
1
852,876,782,465,843,200
عبد الرحمن
9349
عبد الرحمن
false
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 12:57:13
Right, put it there
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 12:57:33
put $f(\alpha) = 0$ and put $f(\beta) = 0$
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
510,789,298,321,096,700
TeXit
01/28/2022 12:57:35
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
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345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 12:58:08
Then simplify and solve till you get $\alpha + \beta$ in terms of "a" and $\alpha \beta$ in terms of "b"
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
510,789,298,321,096,700
TeXit
01/28/2022 12:58:11
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
null
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null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:00:46
nothing... wrong channel ^^"
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:00:53
try that and let me know
0
1
null
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345
help-10
de8c8807f5e141cfa82c416d0506b750
852,876,782,465,843,200
عبد الرحمن
01/28/2022 13:02:26
Should I complete the square ? And find it ?
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:03:00
Nope... Just plug in alpha and beta and tell me what you get
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:04:18
Yeah!
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:04:34
Now eliminate "b" first because you only want a relation in "a", "alpha" and "beta"
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:07:24
yep
0
1
852,876,782,465,843,200
عبد الرحمن
9349
عبد الرحمن
false
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:11:01
$3\alpha^2 + 2a * \alpha + b = 0 \to (1)$ $3\beta^2 + 2a * \beta + b = 0 \to (2)$
0
1
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345
help-10
de8c8807f5e141cfa82c416d0506b750
510,789,298,321,096,700
TeXit
01/28/2022 13:11:22
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
null
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:11:36
Subtract equation 1 from equation 2
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:12:23
$3(\beta^2 -\alpha^2) + 2a(\beta - \alpha) =0$
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
510,789,298,321,096,700
TeXit
01/28/2022 13:12:29
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
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null
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:13:14
factorize and you have
0
1
null
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:13:39
$(\beta - \alpha)(3(\beta + \alpha) + 2a) =0$
0
1
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null
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help-10
de8c8807f5e141cfa82c416d0506b750
510,789,298,321,096,700
TeXit
01/28/2022 13:13:42
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:13:45
So
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:13:57
$3(\beta + \alpha) + 2a =0$
0
1
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null
345
help-10
de8c8807f5e141cfa82c416d0506b750
510,789,298,321,096,700
TeXit
01/28/2022 13:13:59
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:14:04
And
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:14:21
$\beta + \alpha = \frac{-2a}{3}$
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
510,789,298,321,096,700
TeXit
01/28/2022 13:14:25
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:14:30
that's it
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:14:57
For $\alpha \beta$, you just eliminate "a" from the two equations, and you'll get "b" in terms of the roots
0
1
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345
help-10
de8c8807f5e141cfa82c416d0506b750
510,789,298,321,096,700
TeXit
01/28/2022 13:15:00
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
852,876,782,465,843,200
عبد الرحمن
01/28/2022 13:24:09
@Ansh_
0
1
null
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null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:24:21
nope
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:24:30
$(\beta - \alpha)(3(\beta + \alpha) + 2a) =0$
0
1
null
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null
345
help-10
de8c8807f5e141cfa82c416d0506b750
510,789,298,321,096,700
TeXit
01/28/2022 13:24:33
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
null
null
null
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345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:24:55
But questions says beta and alpha are distinct, so (beta - alpha) can't be 0
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:25:01
but the product is zero
0
1
706,934,233,012,371,600
Ansh_
3502
Arya
false
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:25:18
then, what term in the product **must** be zero?
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:25:50
exactly
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:25:54
well done
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:31:17
Again
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:31:18
$3\alpha^2 + 2a * \alpha + b = 0 \to (1)$ $3\beta^2 + 2a * \beta + b = 0 \to (2)$
0
1
null
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null
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:31:20
Right?
0
1
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null
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help-10
de8c8807f5e141cfa82c416d0506b750
510,789,298,321,096,700
TeXit
01/28/2022 13:31:21
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
null
null
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null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:32:10
Now, subtracting equation 1, from equation 2, eliminated "b", why?
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:33:00
Why did eqn. 2 - eqn. 1 work out though?
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:33:03
to eliminate b?
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:34:13
Partially true, but also because the coefficients of "b" were equal in both equation
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:34:45
coefficients is just a term coined to the "factors" multiplied with the _term in concern_ at the moment
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:37:14
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:37:27
Divide eqn. (1) by alpha and eqn. (2) by beta
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
510,789,298,321,096,700
TeXit
01/28/2022 13:38:53
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:39:20
Now can you eliminate "a" from equations 3 and 4?
0
1
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help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:46:10
Lol
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:46:43
You could just do Eqn. 4 - Eqn. 3, eliminate "a" and solve for "b"
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 13:46:51
We're quite literally done here
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 14:03:40
wrong
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 14:03:58
3(alpha - beta) + b/alpha - b/beta = 0
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 14:04:07
now solve for "b"
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 14:18:55
$3(\alpha - \beta) + b/\alpha - b/\beta = 0$
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
510,789,298,321,096,700
TeXit
01/28/2022 14:19:12
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 14:20:00
$\implies 3(\alpha - \beta) - \frac{b(\alpha - \beta)}{\alpha \beta}= 0$
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
510,789,298,321,096,700
TeXit
01/28/2022 14:20:13
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 14:20:52
$\implies (\alpha - \beta)\qty[3 - \frac{b}{\alpha \beta}]= 0$
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
510,789,298,321,096,700
TeXit
01/28/2022 14:20:55
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 14:21:16
$\implies 3 - \frac{b}{\alpha \beta}=0$
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
510,789,298,321,096,700
TeXit
01/28/2022 14:21:19
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 14:21:23
Solve the rest
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 14:21:33
and go through all the steps till you can convince yourself
0
1
null
null
null
null
null
345
help-10
de8c8807f5e141cfa82c416d0506b750
706,934,233,012,371,600
Ansh_
01/28/2022 14:21:35
:D
0
1
null
null
null
null
null
346
help-10
8bfd22019658445785249d01837ac54d
929,960,101,157,146,600
yk
01/28/2022 15:24:53
if a plane contains a line, does that mean the line lies in the plane or the line intersects the plane once?
1
0
null
null
null
null
null
346
help-10
8bfd22019658445785249d01837ac54d
929,960,101,157,146,600
yk
01/28/2022 15:25:19
sorry for pinging @A Lonely Bean I was in class so the channel automatically closed. I reworded my question
1
0
null
null
null
null
null
346
help-10
8bfd22019658445785249d01837ac54d
872,024,354,572,103,700
<><><>
01/28/2022 15:25:34
if a plane contains a line, does that mean the line lies in the plane
0
1
null
null
null
null
null
346
help-10
8bfd22019658445785249d01837ac54d
872,024,354,572,103,700
<><><>
01/28/2022 15:25:40
true
0
1
null
null
null
null
null
346
help-10
8bfd22019658445785249d01837ac54d
929,960,101,157,146,600
yk
01/28/2022 15:28:12
for one of my homework though, the plane "contains" the line but only intersects it once?
https://cdn.discordapp.c…4328/unknown.png
unknown.png
1
0
null
null
null
null
null
346
help-10
8bfd22019658445785249d01837ac54d
872,024,354,572,103,700
<><><>
01/28/2022 15:29:51
not possible
0
1
null
null
null
null
null
346
help-10
8bfd22019658445785249d01837ac54d
929,960,101,157,146,600
yk
01/28/2022 15:30:56
that is so weird then if it is correct then
1
0
348,696,743,388,381,200
A Lonely Bean
7998
A Lonely Bean
false