Question

If ${20}^{3-2x^2}=(40\sqrt{5}{)}^{3x^2-2}$, then the value of $x$ is

• A. $\pm \sqrt{\frac{13}{2}}$
• B. $\pm \sqrt{\frac{12}{13}}$
• C. $\pm \sqrt{\frac{4}{5}}$
• D. $\pm \sqrt{\frac{5}{4}}$

Answer 1

The correct option is B $\pm \sqrt{\frac{12}{13}}$

Given :

$(20{)}^{3-2x^2}=(40\sqrt{5}{)}^{3x^2-2}$

$\Rightarrow (20{)}^{3-2x^2}=(20{)}^{3/2}(3x^2-2)$

$\Rightarrow 3-2x^2=\frac{9x^2-6}{2}$

$\Rightarrow 6-4x^2=9x^2-6$

$\Rightarrow 13x^2=12$

$\Rightarrow x=\pm \sqrt{12/13}$