Question

Evaluate:

$\begin{array}{cc}& 6(9k^2+2)=2(6k+2{)}^2\\ & 54k^2+12=2(36k^2+24k+4)\end{array}$

Answer 1

Given equation

$6(9k^2+2)=2(6k+2{)}^2$

$\Rightarrow 54k^2+12=2(36k^2+24k+4)$

$\Rightarrow 54k^2+12=72k^2+48k+8$

$\Rightarrow 54k^2-72k^2-48k+12-8=0$

$\Rightarrow -18k^2-48k+4=0$

$\Rightarrow 9k^2+24k-2=0$

$\Rightarrow (3k{)}^2+2.3k.4+16-18=0$

$\Rightarrow (3k+4{)}^2-18=0$

$\Rightarrow (3k+4{)}^2=18$

$\Rightarrow 3k+4=\pm \sqrt{18}$

$\Rightarrow 3k=-4\pm 3\sqrt{2}$

$\Rightarrow k=\frac{-4\pm 3\sqrt{2}}{3}$

$k=(\frac{-4}{3}+\sqrt{2}),(\frac{-4}{3}-\sqrt{2})$