[ASK] Power Question

Apr 2018
182
38
Sukoharjo
If \(\displaystyle 4^x+4^{-x}=8\), then \(\displaystyle 8^x+8^{-x}=?\)
A. 14
B. 15
C. 16
D. 17
E. 18

What should I do? I tried substituting \(\displaystyle y = 4^x\) but it didn't help since the quadratic equation formed didn't have real roots.
 

romsek

MHF Helper
Nov 2013
6,758
3,041
California
I get that if $2\cosh(\ln(4)x) = 8$ then $2\cosh(\ln(8)x)\approx 22.1359$

This doesn't match any of the choices.
 
Jun 2013
1,134
605
Lebanon
try the substitution \(\displaystyle y=2^x\)

answer: \(\displaystyle 7 \sqrt{10}\)
 
Apr 2018
182
38
Sukoharjo
Ah, okay then. Thanks to both of you.