Question

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

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

Answer 1

The correct option is B $\pm 1$

$7^{1+x}+7^{1-x}=50$

$7(7^x+7^{-x})=50$

$7\left(7^{2x}\right)+7=50\left(7^x\right)$

$⟹(7^x-7)(7^{x+1}-1)=0$

$⟹7^x=7^1$ or $7^{x+1}=7^0⟹x=\pm 1$