x^4 + y^4 = 100 what is the greatest value of x between?

[lpelaez]

answer is between 3 to 6. how do i solve this for x maximum?

thanks in advance.

[TakingGMAT]

For maximum value of X, take minimum value for y. So take y=1
now x^4=100-1=99
x= 99^1/4 = 3.15 ....
so value of x lies between 3 to 6

[esledge]

Actually, the minimum value for y^4 is 0, as y can be anything and y^4 cannot be negative.

But the logic is the same:
max x^4 + min y^4 = 100
max x^4 + 0 = 100
max x^2 = sqrt(100) = 10
max x = sqrt(10) = more than 3 but less than 4.

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