Question

If $x=2+2^{2/3}+2^{1/3}$, then the value of $x^3-6x^2+6x$ is

• A. $3$
• B. $2$
• C. $1$
• D. None of these

Answer 1

The correct option is B $2$

Given, $x=2+2^{2/3}+2^{1/3}$

$\Rightarrow (x-2)=2^{2/3}+2^{1/3}$

$\Rightarrow (x-2)=2^{2/3}+2^{1/3}$

On cubing both sides, we get

$(x-2{)}^3=2^2+2+3\cdot 2^{2/3}\cdot 2^{1/3}(2^{2/3}+2^{1/3})$

$\Rightarrow x^3-6x^2+12x-8=4+2+3\times 2\times (x-2)$

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