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Please find the attached pict. How (B) could be an answer? Consider x=5.5, then x^4 is already bigger than 100. And y^4 can't be -ve.

If x^4+y^4=100, then the greatest possible value of x is between A. 0 and 3 B. 3 and 6 C. 6 and 9 D. 9 and 12 E. 12 and 15

General rule for such kind of problems: to maximize one quantity, minimize the others; to minimize one quantity, maximize the others.

So, to maximize \(x\) we should minimize \(y^4\). Least value of \(y^4\) is zero. In this case \(x^4+0=100\) --> \(x^4=100\) --> \(x^2=10\) --> \(x=\sqrt{10}\approx{3.2}\), which is in the range (3,6).

\(x^4 + y^4 = 100\) When you see even powers, first thing that should come to your mind is that the term will be positive or zero. If you want to maximize x in the sum, you should minimize y^4 so that this term's contribution in 100 is minimum possible. Since it is an even power, its smallest value is 0 when y = 0.

Then \(x^4\) = 100 Since \(3^4 = 81\) and \(4^4 = 256\),x will lie between 3 and 4.
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Re: If x^4 + y^4 = 100, then the greatest possible value of x [#permalink]

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10 Apr 2012, 08:35

Two things that we must consider in order to solve this problem are:

a) We do not look for an integer

b) We do not look for a specific number but we want to see the number we are looking for in what range falls....e.x it is positive ot it is greater than 10.....in our example all the answers give range....

solution has been given by minimizing Y meaning Y=0

Re: If x^4 + y^4 = 100, then the greatest possible value of x [#permalink]

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08 Aug 2015, 11:50

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Dear Bunuel. i learnt that x square is IxI = + or - or absolute value of X. right ? if right so why here we assume that X = +ve 3.2 ?

That is because of the options provided are positive ranges. You dont want to spend time on irrelevant things such as the negative values.
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