Question

If $3^{2x}+9=10\left(3^x\right)$, then the value of $x^2+1$ is

• A. 1 only
• B. 5 only
• C. 1 or 5
• D. 2

Answer 1

Answer: (C)

1 or 5

$3^{2x}+9=10\left(3^x\right)$

Substituting $3^x=t$, we get

$\Rightarrow$ $t^2+9=10t$

$\Rightarrow$ $t^2-10t+9=0$

$\Rightarrow$ $t^2-9t-t+9=0$

$\Rightarrow$ $t(t-9)-1(t-9)=0$

$\Rightarrow$ $(t-9)(t-1)=0$

$\Rightarrow$ $t-9=0$ and $t-1=0$

$\Rightarrow$ $t=9$ and $t=1$

Re-substituting value of $t$ we get,

$\Rightarrow$ $3^x=9$ and $3^x=1$

$\Rightarrow$ $3^x=3^2$ and $x=0$

$\Rightarrow$ $so1,5$