Question

Solve : $5^{(x+1)}+5^{(2-x)}=5^3+1$

Answer 1

Let $5^x=t$

$5t+\frac{25}{t}=126$

$5t^2-126t+25=0$

$5t^2-125t-t+25=0$

$5t(t-25)-1(t-25)=0$

$(5t-1)(t-25)=0$

$t=5^{-1},5^2$

And $t=5^x$

So $x=-1,2$