Question

Solve for x :-

$\sqrt{3}{x}^2-2\sqrt{2}x-2\sqrt{3}=0$

Answer 1

$\sqrt{3}{x}^2$ $-$ $2\sqrt{2}x$ $-$ $2\sqrt{3}$ $=$ $0$

$Multiplying$ $the$ $equation$ $throughout$ $by$ $\sqrt{3},$

$3x^2$ $-$ $2\times \sqrt{3}\times \sqrt{2}\times x$ $-$ $6$ $=$ $0$

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

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

$(\sqrt{3}x-\sqrt{2}{)}^2$ $=$ $8$

$(\sqrt{3}x-\sqrt{2})$ $=$ $8$

$Or,$

$(\sqrt{3}x-\sqrt{2})$ $=$ $-8$

$Therefore,$

$x$ $=$ $\frac{(8+\sqrt{2})}{\sqrt{3}}$

$Or,$

$x$ $=$ $\frac{(-8+\sqrt{2})}{\sqrt{3}}$