Question

A positive number $x$ is multiplied by $2$, and this product is then divided by $3$. If the positive square root of the result of these two operations equals $x$, what is the value of $x$ ?

• A. $\frac{9}{4}$
• B. $\frac{3}{2}$
• C. $\frac{4}{3}$
• D. $\frac{2}{3}$
• E. $\frac{1}{2}$

Answer 1

Answer: (D)

$\frac{2}{3}$

let positive number be x

$\sqrt{\frac{2x}{3}}=x$

squaring on both sides

$\frac{2x}{3}=x^2{x}^2-\frac{2x}{3}=0x(x-\frac{2}{3})=0x=0,\frac{2}{3}$

as x is positive

$x=\frac{2}{3}$