Question

If $3^{1+x}+3^{1-x}=10$, then the values of $x$ are

• A. $1,-1$
• B. $1,0$
• C. $1,2$
• D. $-1,-2$

Answer 1

Answer: (A)

$1,-1$

$3^{1+x}+3^{1-x}=10$
$3\left(3^x\right)+\frac{3}{3^x}=10$
$3\left(3^{2x}\right)+3={10.3}^x$
Let
$3^x=t$.
Then the above equation changes to
$3\left(t^2\right)+3=10t$
$3t^2-10t+3=0$
$3t^2-9t-t+3=0$
$3t(t-3)-1(t-3)=0$
$(3t-1)(t-3)=0$
$t=\frac{1}{3},3$
Or
$3^x=\frac{1}{3}$ and $3^x=3$
Or
$x=-1,1$.