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help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 22:39:30
yes
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help-1
acc42364cb8e4427a98aeaba7f33596a
869,532,694,688,706,600
EpsilonNought
01/16/2022 22:39:30
Inequality
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1
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help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 22:39:31
please
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help-1
acc42364cb8e4427a98aeaba7f33596a
869,532,694,688,706,600
EpsilonNought
01/16/2022 22:39:33
I love
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1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:39:35
maximize a + b
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help-1
acc42364cb8e4427a98aeaba7f33596a
869,532,694,688,706,600
EpsilonNought
01/16/2022 22:39:43
Link me the question pls
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:39:53
.
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1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:40:04
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
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acc42364cb8e4427a98aeaba7f33596a
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Peppermint Demon
01/16/2022 22:40:17
that is a nice form
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help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 22:40:20
This is the form we transformed it to
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869,532,694,688,706,600
EpsilonNought
01/16/2022 22:40:23
https://cdn.discordapp.c…9772/unknown.png
unknown.png
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acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 22:40:25
Yea
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EpsilonNought
01/16/2022 22:40:57
Hmm
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help-1
acc42364cb8e4427a98aeaba7f33596a
869,532,694,688,706,600
EpsilonNought
01/16/2022 22:41:04
My gut tells me AM-GM inequality
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acc42364cb8e4427a98aeaba7f33596a
869,532,694,688,706,600
EpsilonNought
01/16/2022 22:41:08
Gotta make it that
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Peppermint Demon
01/16/2022 22:42:34
how tho
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EpsilonNought
01/16/2022 22:42:40
I’m trying
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acc42364cb8e4427a98aeaba7f33596a
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Peppermint Demon
01/16/2022 22:42:48
ok 👍
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help-1
acc42364cb8e4427a98aeaba7f33596a
869,532,694,688,706,600
EpsilonNought
01/16/2022 22:42:52
There’s always some trick in such questions
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help-1
acc42364cb8e4427a98aeaba7f33596a
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Peppermint Demon
01/16/2022 22:42:56
true
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acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:43:12
Ok I have a handwavy argument
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:43:16
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
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acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:43:22
We are trying to maximize a + b
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:43:27
this is a linear thing.
0
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:43:44
(a - 2)^2 and (b-2)^2 will grow quadratically
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Shuri2060
01/16/2022 22:43:53
To maintain equality, you have to keep them minimized basically
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:43:57
Handwavy argument, done.
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LittleMouse
01/16/2022 22:44:18
I am so stupid and can't think how to do this
https://cdn.discordapp.c…9610/unknown.png
unknown.png
1
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321,445,119,171,756,000
Shuri2060
01/16/2022 22:44:25
Ok, so did u
0
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:44:29
use quadratic formula
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help-1
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321,445,119,171,756,000
Shuri2060
01/16/2022 22:44:43
Or can't figure it
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help-1
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551,269,104,800,104,450
EndTimes
01/16/2022 22:44:48
Expand (x+y)^2
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help-1
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551,269,104,800,104,450
EndTimes
01/16/2022 22:44:52
do it.
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:44:56
???
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Shuri2060
01/16/2022 22:45:03
well ok
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acc42364cb8e4427a98aeaba7f33596a
782,087,086,416,461,800
LittleMouse
01/16/2022 22:45:05
** **
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
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Shuri2060
01/16/2022 22:45:09
Hint: let y be constant.
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help-1
acc42364cb8e4427a98aeaba7f33596a
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Shuri2060
01/16/2022 22:45:43
are u sure this helps???
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LittleMouse
01/16/2022 22:46:52
no idea
1
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acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:47:09
try what I said. Quadratic formula.
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help-1
acc42364cb8e4427a98aeaba7f33596a
782,087,086,416,461,800
LittleMouse
01/16/2022 22:47:24
how to apply it 😦
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GigaChad
5823
GigaChad
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205,444
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Geopchad
01/16/2022 22:47:29
take y as a constant
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:47:30
let y be constant
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
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Geopchad
01/16/2022 22:47:31
like shuri said
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help-1
acc42364cb8e4427a98aeaba7f33596a
328,662,734,008,746,000
Geopchad
01/16/2022 22:47:45
and then you wanna move the 2 to the x side and then use the quadratic formula
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help-1
acc42364cb8e4427a98aeaba7f33596a
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LittleMouse
01/16/2022 22:48:46
https://cdn.discordapp.c…3338/unknown.png
unknown.png
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0
404,260,981,385,068,540
I've Psychosis & OCD
3754
I've Psychosis & OCD
false
205,444
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Shuri2060
01/16/2022 22:49:03
yh
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Camilleone
01/16/2022 22:49:46
I sort of have a solution, but it's a bit backwards
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help-1
acc42364cb8e4427a98aeaba7f33596a
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Shuri2060
01/16/2022 22:50:00
👂
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EpsilonNought
01/16/2022 22:50:49
Sure
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help-1
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Shuri2060
01/16/2022 22:50:59
$$\frac{1}{(a-2)^2 + 4(a+b) + \epsilon\left(2a+\epsilon\right)} + \frac{1}{(b-2)^2 + 4(a+\epsilon+b)} = \frac{1}{8}$$
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help-1
acc42364cb8e4427a98aeaba7f33596a
510,789,298,321,096,700
TeXit
01/16/2022 22:51:02
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
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Shuri2060
01/16/2022 22:51:09
subbing a + e in case it helps
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
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Peppermint Demon
01/16/2022 22:51:37
wut
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I've Psychosis & OCD
3754
I've Psychosis & OCD
false
205,444
help-1
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Peppermint Demon
01/16/2022 22:51:45
where did you sub a+e?
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:51:51
to the original thing.
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1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:51:57
thats after rearranging
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 22:52:00
instead of a?
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:52:03
yes
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 22:52:06
ah
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1
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help-1
acc42364cb8e4427a98aeaba7f33596a
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Camilleone
01/16/2022 22:52:51
Claim: 4(a+b) cannot exceed 16. Proof: Suppose it does, then it must be the case that at least one of (a-2)^2, (b-2)^2 is positive. Then both fractions are < 1/16 so equality to 1/8 cannot hold
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acc42364cb8e4427a98aeaba7f33596a
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Camilleone
01/16/2022 22:53:09
Hence a+b is at most 4
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help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 22:53:30
It remains to find a and b - possible with a=b=2
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help-1
acc42364cb8e4427a98aeaba7f33596a
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Camilleone
01/16/2022 22:54:05
In fact the claim proof can be shorter
0
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:54:12
Is not backwards. You are just using 👀 on factorisation
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help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 22:55:03
oh damn
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acc42364cb8e4427a98aeaba7f33596a
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Camilleone
01/16/2022 22:55:08
The nonneg squares are enough, so: Suppose not. Squares are nonneg so both fractions are < 1/16, so the sum cannot be 1/8
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help-1
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LittleMouse
01/16/2022 22:55:22
https://cdn.discordapp.c…0851/unknown.png
unknown.png
1
0
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acc42364cb8e4427a98aeaba7f33596a
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Shuri2060
01/16/2022 22:55:36
yes
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
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Camilleone
01/16/2022 22:55:51
Did we finish it? Yes yes?
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
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Camilleone
01/16/2022 22:55:58
I think we have
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 22:56:05
lets gooo
0
1
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Shuri2060
01/16/2022 22:56:12
i think i can do perturbation analysis argument
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
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Peppermint Demon
01/16/2022 22:56:21
what thefric
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
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Camilleone
01/16/2022 22:56:25
LOL
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1
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Camilleone
01/16/2022 22:56:34
Might as well go the whole way
0
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help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 22:56:39
Lagrange multipliers ftw
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 22:56:59
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
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LittleMouse
01/16/2022 22:57:45
what should i do with this
1
0
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acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:57:46
no nvm, idk wtf I did
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:57:53
factorise
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:57:59
inside the root is ugly thing
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:58:04
wait no im dumb
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1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:58:08
well 1. yes factorise
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1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:58:13
2., think discriminant
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:58:18
for x to be real
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:58:20
what must be true
0
1
404,260,981,385,068,540
I've Psychosis & OCD
3754
I've Psychosis & OCD
false
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
782,087,086,416,461,800
LittleMouse
01/16/2022 22:58:42
the thing under root is pos
1
0
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:58:45
yh ok
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1
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null
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:58:48
$$\frac{1}{(a-2)^2 + 4(a+b) + \epsilon\left(2a+\epsilon\right)} + \frac{1}{(b-2)^2 + 4(a+b)+4\epsilon} = \frac{1}{8}$$
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help-1
acc42364cb8e4427a98aeaba7f33596a
510,789,298,321,096,700
TeXit
01/16/2022 22:58:50
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:58:55
@Camilleone Is this even possible
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:58:58
or did I make mistake
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:59:03
i sub a -> a + e
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:59:17
oh nvm nvm nvm
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1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:59:32
can i even say anything here though
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 22:59:47
Not anything immediately, no
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 22:59:51
💤
0
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help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 23:00:09
Perturbation argument is the same as the sturm-liouville method we talked about briefly
0
1
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null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:00:15
yh
0
1
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