If a - frac{1}{a - 3} = 5,then the value of ( | vedclass

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(D) Given equation: $a - \frac{1}{a - 3} = 5$Subtracting $3$ from both sides,we get:$(a - 3) - \frac{1}{a - 3} = 5 - 3$$(a - 3) - \frac{1}{a - 3} = 2$

Vedclass · Accepted Answer

$14$

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(D) Given equation: $a - \frac{1}{a - 3} = 5$Subtracting $3$ from both sides,we get:$(a - 3) - \frac{1}{a - 3} = 5 - 3$$(a - 3) - \frac{1}{a - 3} = 2$Let $x = (a - 3)$. Then the equation becomes $x - \frac{1}{x} = 2$.We know the algebraic identity: $x^{3} - \frac{1}{x^{3}} = (x - \frac{1}{x})^{3} + 3(x - \frac{1}{x})$.Substituting $x - \frac{1}{x} = 2$ into the identity:$x^{3} - \frac{1}{x^{3}} = (2)^{3} + 3(2)$$x^{3} - \frac{1}{x^{3}} = 8 + 6 = 14$.Therefore,the value of $(a - 3)^{3} - \frac{1}{(a - 3)^{3}}$ is $14$.

If $a - \frac{1}{a - 3} = 5$,then the value of $(a - 3)^{3} - \frac{1}{(a - 3)^{3}}$ is

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