Question

Solve the following equations:
$5(5^x+5^{-x})=26$.

• A. $1,2$
• B. $\pm 1$
• C. $2,-1$
• D. $1,-2$

Answer 1

Answer: (B)

$\pm 1$

Given,, $5(5^x+5^{-x})=26$

$\Rightarrow 5(5^x+\frac{1}{5^x})=26$

Put $5^x=t$

$5(t+\frac{1}{t})=26$

Therefore, $5t^2+5=26t$

$\Rightarrow 5t^2-26t+5=0$

$\Rightarrow 5t^2-25t-t+5=0$

$\Rightarrow (5t-1)(t-5)=0$

$\Rightarrow t=5,\frac{1}{5}$

Resubstituting the value, we get

$5^x=t$

$\Rightarrow 5^x=5=5^1$

$\Rightarrow x=1$

$\Rightarrow 5^x=\frac{1}{5}=5^{-1}$

$\Rightarrow x=-1$

So, complete solution is $x=\pm 1$.