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help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 23:00:43
So do you want to do the honours of writing out a proper argument?
0
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:00:54
what
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:00:56
u wrote it
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:00:56
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 Hence a+b is at most 4 It remains to find a and b - possible with a=b=2 In fact the claim proof can be shorter
0
1
692,059,999,073,206,400
GigaChad
5823
GigaChad
false
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 23:01:00
Yep
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:01:07
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 23:01:12
op
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 23:01:12
I meant to batch the whole thing together
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:01:14
Let me check thru it
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:01:41
1 / (? + 16>) + 1 / (? + 16>)
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
782,087,086,416,461,800
LittleMouse
01/16/2022 23:01:58
https://cdn.discordapp.c…7515/unknown.png
unknown.png
1
0
null
null
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:01:58
'at least one of (a-2)^2, (b-2)^2 is positive'
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:02:03
👌
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 23:02:08
nice
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:02:11
I don't understand this @Camilleone
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 23:02:19
No need
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:02:19
one of them must be positive regardless, what
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:02:29
ok ok ok
0
1
null
null
null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 23:02:30
See the shorter claim proof
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 23:02:53
the proof was smart af
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:02:58
Claim: a + b <= 16 Suppose it doesn't. Squares are nonneg so both fractions are < 1/16, so the sum cannot be 1/8
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
782,087,086,416,461,800
LittleMouse
01/16/2022 23:03:05
then:?
1
0
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:03:05
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
0
1
null
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:03:11
kk nice
0
1
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null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:03:15
yessssssssss
0
1
null
null
null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:03:25
https://cdn.discordapp.c…7964/unknown.png
unknown.png
0
1
null
null
null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:03:32
sketch graph?
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 23:03:32
:satisfiedblob:
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:03:34
wait what
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:03:40
wait a minute
0
1
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null
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 23:03:43
i think it should be "suppose it doesn't"?
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:03:51
How did u get the 2nd inequality
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
782,087,086,416,461,800
LittleMouse
01/16/2022 23:04:06
square both side
1
0
null
null
null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:04:12
wat
0
1
null
null
null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 23:04:17
Yeah, good typo catch
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:04:18
in the first place thats not what u should write
0
1
null
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
328,662,734,008,746,000
Geopchad
01/16/2022 23:04:18
when you divide by a negative for inequalities you haev to flip the sign
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:04:26
We need discriminant
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
328,662,734,008,746,000
Geopchad
01/16/2022 23:04:27
4 > 3
0
1
null
null
null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
328,662,734,008,746,000
Geopchad
01/16/2022 23:04:29
-4 < -3
0
1
null
null
null
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 23:04:32
also > y-3
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:04:35
The **inside** of the squareroot >= 0
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:04:46
=> ...
0
1
null
null
null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
782,087,086,416,461,800
LittleMouse
01/16/2022 23:04:51
yaa
1
0
null
null
null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:05:03
$$-3(y+3)(y-1)\geq 0$$
0
1
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null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
510,789,298,321,096,700
TeXit
01/16/2022 23:05:06
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
0
1
null
null
null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
782,087,086,416,461,800
LittleMouse
01/16/2022 23:05:06
ok
1
0
null
null
null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:05:32
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
0
1
null
null
null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:05:36
Ok so lets construct a new Q
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:05:38
thats harder
0
1
null
null
null
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:05:41
like this one
0
1
null
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null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 23:05:42
why
0
1
null
null
null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:05:45
why not
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 23:05:49
because pain
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 23:05:53
ok go ahead
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
328,662,734,008,746,000
Geopchad
01/16/2022 23:06:37
yoooo
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
328,662,734,008,746,000
Geopchad
01/16/2022 23:06:40
shuri got very active!!
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 23:06:41
I know a repository for painful questions - the international mathematics competition for university students
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
869,532,694,688,706,600
EpsilonNought
01/16/2022 23:06:42
Yoooo
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:06:46
lol wut
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:06:50
these roles are hacked
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
328,662,734,008,746,000
Geopchad
01/16/2022 23:06:51
that's crazy
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
328,662,734,008,746,000
Geopchad
01/16/2022 23:07:03
we gotta celebrate
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:07:11
https://i.imgur.com/0jmTXjT.png
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:07:14
how does it even count
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:07:16
👀
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 23:07:18
Wooooooo
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 23:07:22
yoooo
0
1
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null
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:07:24
🥳
0
1
null
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null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 23:08:05
wait what
0
1
null
null
null
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 23:08:32
oh right
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 23:08:35
i read that as IMO
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:08:55
$$\frac{1}{(a-2)^2 + 4(a+b+c)} + \frac{1}{(b-2)^2 + 4(a+b+c)} + \frac{1}{(c-2)^2 + 4(a+b+c)} = \frac{1}{72}$$
0
1
null
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null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:08:57
Does this work
0
1
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null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
510,789,298,321,096,700
TeXit
01/16/2022 23:08:57
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
0
1
null
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null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:09:05
urgh
0
1
null
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null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
869,532,694,688,706,600
EpsilonNought
01/16/2022 23:09:09
Where did c come from
0
1
null
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 23:09:20
we making new question
0
1
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205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:09:32
$$\frac{1}{(a-2)^2 + 4(a+b+c)} + \frac{1}{(b-2)^2 + 4(a+b+c)} $$ $$+ \frac{1}{(c-2)^2 + 4(a+b+c)} = \frac{1}{72}$$
0
1
null
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null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
510,789,298,321,096,700
TeXit
01/16/2022 23:09:35
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
0
1
null
null
null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 23:10:01
Wat
0
1
null
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null
null
null
205,444
help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:10:03
Then present with the fractions multiplied out lol
0
1
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:10:19
'Suppose a + b + c > 6'
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:10:24
right?
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:10:37
ohwoops
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:10:38
1/8
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1
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help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 23:10:41
Then you can't exceed 3/24 = 1/8
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help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 23:10:46
Hoho
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:10:47
1/24 + 1/24 + 1/24 = 1/72
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:10:48
gg
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:10:52
$$\frac{1}{(a-2)^2 + 4(a+b+c)} + \frac{1}{(b-2)^2 + 4(a+b+c)} $$ $$+ \frac{1}{(c-2)^2 + 4(a+b+c)} = \frac{1}{8}$$
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help-1
acc42364cb8e4427a98aeaba7f33596a
510,789,298,321,096,700
TeXit
01/16/2022 23:10:54
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
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help-1
acc42364cb8e4427a98aeaba7f33596a
782,087,086,416,461,800
LittleMouse
01/16/2022 23:11:00
https://cdn.discordapp.c…6702/unknown.png
unknown.png
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:11:06
NO
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:11:09
bad
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1
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help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 23:11:11
bruhh
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help-1
acc42364cb8e4427a98aeaba7f33596a
912,292,630,036,099,100
Peppermint Demon
01/16/2022 23:11:12
lmao
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:11:15
terrible
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help-1
acc42364cb8e4427a98aeaba7f33596a
321,445,119,171,756,000
Shuri2060
01/16/2022 23:11:20
graph sketch
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help-1
acc42364cb8e4427a98aeaba7f33596a
569,167,697,925,898,240
Camilleone
01/16/2022 23:11:21
I like this question, vairy nice
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