Question

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

Answer: (B)

$\pm \sqrt{\frac{12}{13}}$

The given equation may be written as $(4\times 5{)}^{3-2x^2}=(8\times 5\sqrt{5}{)}^{{3x}^2-2}\Rightarrow (2\sqrt{5}{)}^{2(3-{2x}^2)}=(2\times \sqrt{5}{)}^{3({3x}^2-2)}\Rightarrow 6-4x^2={9x}^2-6\Rightarrow 13x^2=12\Rightarrow x=+\sqrt{\frac{12}{13}}or-\sqrt{\frac{12}{13}}$