Question

Evaluate:$\frac{1}{\sqrt{x^2+2x+9}}=1$

Answer 1

$\frac{1}{\sqrt{x^2+2x+9}}=1$

$\Rightarrow \sqrt{x^2+2x+9}=1$

$\Rightarrow x^2+2x+9-1=0$

$\Rightarrow x^2+2x+8=0$

$\Rightarrow x^2+2\times 1\times x+1-1+8=0$

$\Rightarrow {(x+1)}^2+7=0$

$\Rightarrow {(x+1)}^2=-7$

$\Rightarrow x+1=\pm \sqrt{-7}$

$\therefore x=-1\pm i\sqrt{7}$