Value of n for which given expression is a perfect cube

$\begingroup$

Find a natural number n such that the expression $3^9+3^{12}+3^{15}+3^n$is a perfect cube. I converted expression to $3^9(1+3^3+3^6+3^{n-9}).$ Clearly if we prove the expression in bracket to be a perfect cube, we can prove the expression as a whole to be a perfect cube, but I cannot prove the expression in bracket to be a cube further. Please help!

$\endgroup$ 1

1 Answer

$\begingroup$

Try to expand $(1+3^2)^3$ and compare with your expression.

$\endgroup$ 4

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy