Solving for x in n + n^(1/2) + n^(1/3) = 76

[Kushal]

Homework Statement

let x and y be positive integers and n = x^y
If n + n^(1/2) + n ^(1/3) = 76, then x cannot equal
A. 64
B. 16
C. 8
D. 4
E. 2

Homework Equations

The Attempt at a Solution

i really don't know how to approach this question. i tried simplifying the powers and write them in terms of x and y, e.g. x^y + x^(y/2) + x ^(y/3) = 76 and i expressed the answers as powers of 2 but i couldn't find a way out.

 

[quantumdude]

Start by letting x=64. Then by inspection it is clear that for y=1, you get 76. Then try to express 64 as integer powers of the other answer choices. If you do that then you will find the one answer choice that doesn't work by exhausting the answer choices that do work.

 

[Kushal]

2, 4 and 8 can be expressed as integer powers of 64. but actually the answer is 8 but not 16... :S

 

[HallsofIvy]

2, 4 and 8 can be expressed as integer powers of 64. but actually the answer is 8 but not 16... :S

And how exactly did you decide that? Since 8²= 64, taking x= 8, y= 2 obviously does satisfy the equation and x= 8 is not the answer.

 

[Kushal]

awww... I'm terribly sorry!

i misread the answer off the book...thanks a loot for helping

 

[HallsofIvy]

Do we get to share in the loot?

 

[Kushal]

ok, loot = lot! ;)