Question

Solve for $x$: $\frac{8\sqrt{x-5}}{3x-7}=\frac{\sqrt{3x-7}}{x-5}$

• A. $13$
• B. $23$
• C. $14$
• D. $-13$

Answer 1

The correct option is A $13$

$\frac{8\sqrt{x-5}}{3x-7}=\frac{\sqrt{3x-7}}{x-5}$

$\Rightarrow 8(x-5{)}^{\frac{3}{2}}=(3x-7{)}^{\frac{3}{2}}$

Squaring on both sides we get,

$\Rightarrow 64(x-5{)}^3=(3x-7{)}^3$

Taking cube roots on both sides, we get

$\Rightarrow 4(x-5)=(3x-7)$

$\Rightarrow 4x-20=3x-7$

$\Rightarrow x=13$

Hence, option A is correct.