Question

Solve the following
$\begin{array}{c}4\sqrt{3}{x}^2+5x-2\sqrt{3}=0\\ 7\sqrt{2}{x}^2-10x-4\sqrt{2}=0\end{array}$

Answer 1

Consider the given equations.

$4\sqrt{3}{x}^2+5x-2\sqrt{3}=0$ ……. (1)

$7\sqrt{2}{x}^2-10x-4\sqrt{2}=0$ ……. (2)

From equation (1)

$4\sqrt{3}{x}^2+5x-2\sqrt{3}=0$

$4\sqrt{3}{x}^2+8x-3x-2\sqrt{3}=0$

$4x(\sqrt{3}x+2)-\sqrt{3}(\sqrt{3}x+2)=0$

$(4x-\sqrt{3})(\sqrt{3}x+2)=0$

$4x-\sqrt{3}=0\Rightarrow x=\frac{\sqrt{3}}{4}$

$\sqrt{3}x+2=0\Rightarrow x=-\frac{2}{\sqrt{3}}$

Now, from equation (2)

$7\sqrt{2}{x}^2-10x-4\sqrt{2}=0$

$7\sqrt{2}{x}^2-14x+4x-4\sqrt{2}=0$

$7\sqrt{2}x(x-\sqrt{2})+4(x-\sqrt{2})=0$

$(7\sqrt{2}x+4)(x-\sqrt{2})=0$

$7\sqrt{2}x+4=0\Rightarrow x=-\frac{4}{7\sqrt{2}}$

$x-\sqrt{2}=0\Rightarrow x=\sqrt{2}$

Hence, this is the answer.