Question

The solution of the equation $7^{1+x}+7^{1-x}=50$ is

• A. $0$
• B. $2$
• C. $\pm 1$
• D. None of these

Answer 1

Answer: (C)

$\pm 1$

$7^{1+x}+7^{1-x}=50$ can be written as
${7.7}^x+\frac{7}{7^x}=50$
Let $7^x$ be t
$7t^2-50t+7=0$
$(t-7)(7t-1)=0$
$\therefore t=7,\frac{1}{7}$
$7^x=7,\frac{1}{7}$
$x=-1,1$