OG10-368 the greatest possible value of x?

[mitzi]

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

My approach to this question is
first of all, when y = 0, then x can have the largest value.
so focus on X^4

3^4 = 81
4^4 = 256 --> it goes over than 100. so I picked a.

However, oa is D.

I don't understand that how the answer can be B. What am I missing here?
Thank you for your help in advance.

Mitzi

[EdYo]

IMO B

I found 1 way to solve it, it sounds strange but it works

rewrite X^4 + Y^4 = 100 ---> (X^2)^2 + (Y^2)^2 = 10^2

Now let say a = X^2, b = Y^2 ---> a^2 + b^2 = 10^2

it looks like Pythagorean to me? so the max i can get here for a falls in the range of 9 -- 10 --> X should falls in the range 3 -- 6

[sonikamadala]

yes it should be B

[mitzi]

EdYo,

Thank you for different ways to look at this! It makes sense.

sonikamadala, Will you share the way you approach to this question? Thank you.

[finsisher]

since u already know that x is greater than 3 but less than 4 so x falls b/w 3 and 6 range so B