If x-2-22 - 3-21 - 3- then the value of x3-6 x2-6 x isA- 3B- 2C- -3D- -2

The correct option is B 2Given: x= 2+ 2^2/3 + 2^1/3 ⇒ x 2 = 2^2/3 + 2^1/3, Cubing the equation on both sides, we get ⇒ (x 2)^3 = 4 +2 + 3× 2^2/3× 2^1/3(2^2/3 + ...

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Byju's Answer

Standard XII

Mathematics

Higher Order Equations

If x=2+22 / 3...

Question

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

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Solution

The correct option is B $2$
Given:
$x = 2 + 2^{2 / 3} + 2^{1 / 3}$
$\Rightarrow x - 2 = 2^{2 / 3} + 2^{1 / 3},$
Cubing the equation on both sides, we get
$\Rightarrow (x - 2)^{3} = 4 + 2 + 3 \times 2^{2 / 3} \times 2^{1 / 3} (2^{2 / 3} + 2^{1 / 3})$
$\Rightarrow x^{3} - 8 + 6 x (x - 2) = 6 + 6 (x - 2)$
$\Rightarrow x^{3} - 6 x^{2} + 12 x - 8 = - 6 + 6 x$
$∴ x^{3} - 6 x^{2} + 6 x = 2$

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If x=2+22/3+21/3, then the value of x3−6x2+6x is

The correct option is B 2Given: x=2+22/3+21/3 ⇒x−2=22/3+21/3, Cubing the equation on both sides, we get ⇒(x−2)3=4+2+3×22/3×21/3(22/3+21/3) ⇒x3−8+6x(x−2)=6+6(x−2) ⇒x3−6x2+12x−8=−6+6x ∴x3−6x2+6x=2

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