Question

Solve:

$\sqrt{2}{x}^2+\sqrt{3}(1-2\sqrt{2})x-6=0$.

Answer 1

$\sqrt{2}{x}^2+\sqrt{3}x+2\sqrt{6}x-6=0\sqrt{2}{x}^2+x(\sqrt{3}-2\sqrt{6})-6=0x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}a=\sqrt{2},b=(\sqrt{3}-2\sqrt{6}),c=-6b^2-4ac=3+24-12\sqrt{2}+24\sqrt{2}={(\sqrt{3}+2\sqrt{6})}^{2}x=\frac{-(\sqrt{3}-2\sqrt{6})\pm (\sqrt{3}+2\sqrt{6})}{2\sqrt{2}}$

Take positive,$x=2\sqrt{3}$

and take negative,$x=\frac{-\sqrt{3}}{\sqrt{2}}$