Question

$3^{\left(x+2\right)}+3^{-x}=10$
Solve using middle term splitting

Answer 1

$3^x=a$, $3^2=9$

$3^{2}a+a^{-1}=10$

$9a+\frac{1}{a}=10$

$9a^2+1=10a$

$9a^2-10a+1=0$

$9a^2-9a-a+1=0$

$9a(a-1)-1(a-1)=0$

$a=\frac{1}{9}$, $a=1$

$a=3^{-2}$, $a=3^o$

$3^x=3^{-2}$, $3^x=3^o$

$x=-2$, $x=0$.