Question

Se 2 elevado a x +2 elevado -x=10 então 4 elevado x + 4 elevado a -x vale :;

a)40
b)50
c)75
d)98
e)100

Answer 1

$2^{x}+2^{-x}=10\\ \\ \left(2^{x}+2^{-x}\right)^{2}=10^{2}\\ \\ 2^{2x}+2\cdot 2^{x}\cdot 2^{-x}+2^{-2x}=100\\ \\ \left(2^{2}\right)^{x}+2^{1+x-x}+\left(2^{2}\right)^{-x}=100\\ \\ 4^{x}+2+4^{-x}=100\\ \\ 4^{x}+4^{-x}=100-2\\ \\ 4^{x}+4^{-x}=98$