If x = sqrt[3]{x^{2} + 11} - 2,then the value | vedclass

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Question

(B) Given the equation: $x = \sqrt[3]{x^{2} + 11} - 2$.Add $2$ to both sides: $x + 2 = \sqrt[3]{x^{2} + 11}$.Cube both sides of the equation: $(x + 2)

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(B) Given the equation: $x = \sqrt[3]{x^{2} + 11} - 2$.Add $2$ to both sides: $x + 2 = \sqrt[3]{x^{2} + 11}$.Cube both sides of the equation: $(x + 2)^{3} = x^{2} + 11$.Expand the left side using the identity $(a + b)^{3} = a^{3} + b^{3} + 3ab(a + b)$:$x^{3} + 2^{3} + 3(x)(2)(x + 2) = x^{2} + 11$.Simplify the expression:$x^{3} + 8 + 6x(x + 2) = x^{2} + 11$.$x^{3} + 8 + 6x^{2} + 12x = x^{2} + 11$.Rearrange the terms to isolate $(x^{3} + 5x^{2} + 12x)$:$x^{3} + 6x^{2} - x^{2} + 12x = 11 - 8$.$x^{3} + 5x^{2} + 12x = 3$.Thus,the value is $3$.

If $x = \sqrt[3]{x^{2} + 11} - 2$,then the value of $(x^{3} + 5x^{2} + 12x)$ is

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