Bunuel wrote:

If a^6 + b^6 = 144 then the greatest possible value for b is between

A. 8 and 10

B. 6 and 8

C. 4 and 6

D. 2 and 4

E. 2 and 0

The question states that \(b^6 = 144-a^6\). Hence for \(b\) to be maximum \(a=0\)

so \(b^6=144\) taking square root of both the sides, we get

\(b^3 = 12\). Now,

\(8<12<27\) or \(8<b^3<27\). Taking cube root of the inequality we get

\(2<b<3\). Hence \(b\) is definitely greater than \(2\) but less than \(3\) (to be precise; \(b^3 = 12\), or \(b= 2.289428\))

Ideally the greatest possible value of \(b\) is between \(2\) & \(3\), but we don't have any option stating that.

Hi

Bunuel can you confirm whether Option

D is correct and there are no typo errors