Find the value of x^{3}-frac{1}{x^{3}} when x | vedclass

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(C) Given that $x-\frac{1}{x}=a$.We know the algebraic identity $(x-y)^{3}=x^{3}-y^{3}-3xy(x-y)$.Substituting $y = \frac{1}{x}$ into the identity,we g

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$a^{3}+3a$

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(C) Given that $x-\frac{1}{x}=a$.We know the algebraic identity $(x-y)^{3}=x^{3}-y^{3}-3xy(x-y)$.Substituting $y = \frac{1}{x}$ into the identity,we get:$\left(x-\frac{1}{x}\right)^{3}=x^{3}-\left(\frac{1}{x}\right)^{3}-3(x)\left(\frac{1}{x}\right)\left(x-\frac{1}{x}\right)$.Simplifying the expression:$\left(x-\frac{1}{x}\right)^{3}=x^{3}-\frac{1}{x^{3}}-3\left(x-\frac{1}{x}\right)$.Now,substitute the given value $x-\frac{1}{x}=a$ into the equation:$a^{3}=x^{3}-\frac{1}{x^{3}}-3(a)$.Rearranging the terms to solve for $x^{3}-\frac{1}{x^{3}}$:$x^{3}-\frac{1}{x^{3}}=a^{3}+3a$.

Find the value of $x^{3}-\frac{1}{x^{3}}$ when $x-\frac{1}{x}=a$.

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