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If x4 + y4 = 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

x4 is x raised to the power of 4 (I could not figure out how to show it as an exponent)

Thanks

Greatest possible value of X when Y^4 is minimum. The possible minimum value of Y^4 is 0 \(X^4=100 ---> X^2=10 --> X> 3 AND X<4\) B is the answer.
_________________

Your attitude determines your altitude Smiling wins more friends than frowning

shailyam, The ans should be B not A since values geater than 3 also satify the equation e.g. x = 3.1 can also be possible.

Going by your logic, one can consider 3.1 as a possible value of x. Here we're not sure of the value of x and saying that the greatest possible value of x is between 3 and 6 would mean that x could be even more than 3.1, for example 4. Hence, answer is A

shailyam, The ans should be B not A since values geater than 3 also satify the equation e.g. x = 3.1 can also be possible.

Going by your logic, one can consider 3.1 as a possible value of x. Here we're not sure of the value of x and saying that the greatest possible value of x is between 3 and 6 would mean that x could be even more than 3.1, for example 4. Hence, answer is A

That's not correct.

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).

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