Question

If $x=2+2^{1/3}{2}^{2/3}$, find the value of $(x^3-6x^2+6x)$

• A. 2
• B. 4
• C. -8
• D. 6

Answer 1

The correct option is C -8

Consider the given equation,

$x=2+2^{\frac{1}{3}}{.2}^{\frac{2}{3}}$

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

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

$x=4$

We have to find the value of ,

$\Rightarrow x^3-6x^2+6x$

Put x=4 ,we get

$x^3-6x^2+6x=4^3-6\times 4^2+6\times 4$

$=64-96+24$

$=-8$

Hence, this is the answer.