Question

Solve: $(2n+7)<(n+3{)}^2$

Answer 1

$2n+7<{(n+3)}^2$

$\Rightarrow 2n+7<n^2+9+6n$

$\Rightarrow n^2+4n+2>0$

Now, adding and subtracting $4$ we get,

$n^2+4n+2+4-4>0$

$\Rightarrow n^2+4n+4-4+2>0$

$\Rightarrow {(n}^2+2\times n\times 2+2^2)-2>0$

$\Rightarrow {(n+2)}^2>2$

$\Rightarrow n+2>\sqrt{2}$

$\Rightarrow n>\sqrt{2}-2$