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# Is x^4 + y^4 > z^4?

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Manager
Joined: 15 Aug 2015
Posts: 62
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Re: Is x^4 + y^4 > z^4?  [#permalink]

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23 Dec 2017, 07:11
walker wrote:
Nice question. Here is my reasoning that allowed me to solve the problem pretty fast.

The inequity true for X=Y=Z=1 --> 1+1>1

Now, let's increase Z (X=Y=1). Z^2 will grow faster than Z but slower than Z^4. So, at some point Z^4 will be greater than 2 but Z^2 and Z will be lesser than 2 and still both conditions will be satisfied. So E.

WOW !!!
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Extra kudos from here !!!!
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Re: Is x^4 + y^4 > z^4?  [#permalink]

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31 Dec 2017, 23:57
for this problem, remember the simple rule

if a number is smaller than 1, the more square, we get smaller number
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Re: Is x^4 + y^4 > z^4?  [#permalink]

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01 Jan 2018, 12:16
Hi thangvietnam,

You have to be careful with your "generalizations." I think what you mean to say is "squaring any positive fraction (meaning 0 < X < 1) will result in a value for X^2 that is smaller than X." Squaring 0 will NOT lead to a smaller result; squaring a negative value will lead to a LARGER result.

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Re: Is x^4 + y^4 > z^4?  [#permalink]

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08 Jan 2018, 09:40
ksharma12 wrote:
Is x^4 + y^4 > z^4?

(1) x^2 + y^2 > z^2
(2) x + y > z

i do this many times
pick z=1
take other x and y values which is greater than 1 and smaller than 1
if x and y are greater than 1, we have YES answer
if x and y are smaller than 1 , we have NO answer.

hard one
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Re: Is x^4 + y^4 > z^4?  [#permalink]

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09 Mar 2018, 20:22
ksharma12 wrote:
Is x^4 + y^4 > z^4?

(1) x^2 + y^2 > z^2
(2) x + y > z

picking specific numbers is best way

take z=1, then pick x,y larger than 1
then pick x,y smaller than 1
Re: Is x^4 + y^4 > z^4? &nbs [#permalink] 09 Mar 2018, 20:22

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