Question

If $x=\sqrt[3]{39\sqrt[3]{39\sqrt[3]{39}.......\infty }}$ then find $x$.

• A. $\sqrt[3]{39}$
• B. $\sqrt[3]{33}$
• C. $0$
• D. $\sqrt{3}$

Answer 1

Answer: (C)

$0$

We have,

$x{=}^3\sqrt{9x}$
$x^3=9x$
$x\left(x^2-9\right)=0$
$x\left(x+3)(x-3\right)=0$
$x=0,\pm 3$

Hence, this is the answer.