Question

If $\sqrt[3]{3\frac{x}{729}}+\sqrt[3]{3\frac{8x}{729}}+\sqrt[3]{3\frac{27x}{5832}}=1$, then find the value of $x$.

• A. $1$
• B. $8$
• C. $3$
• D. $4$

Answer 1

Answer: (B)

$8$

$\sqrt[3]{3\frac{x}{729}}+\sqrt[3]{3\frac{8x}{729}}+\sqrt[3]{3\frac{27x}{5832}}=1$

$\Rightarrow \frac{x^{\frac{1}{3}}}{9}+\frac{2x^{\frac{1}{3}}}{9}+\frac{3x^{\frac{1}{3}}}{18}=1$

$\Rightarrow 2x^{\frac{1}{3}}+4x^{\frac{1}{3}}+3x^{\frac{1}{3}}=18$

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

$\Rightarrow x=8$.