Question

If x-1 by x = 3 then x power 3 - 1 by x power 3 = ?
(a) 27
(b) 18
(c) 30
(d) 36​

Answer 1

Answer:

(a) 27 is the answer of x-1 by x=3 then x power 3-1

Answer 2

$\LARGE{\bf{\underline{\underline{Solution:-}}}}$

${\bf{\underline{\underline{Given:-}}}}$

$\bf{{x - }}$$\bf\dfrac{1}{x}$$\bf{{= 3}}$

${\bf{\underline{\underline{To \ Find:-}}}}$

$\bf{{x^{3} - }}$$\bf\dfrac{1}{x^{3}}$

${\bf{\underline{\underline{Formula \ which \ we \ will \ use:-}}}}$

$\bf{{(x - }}$$\bf\dfrac{1}{x})^{3}$$\bf{{= x^{3} - }}$$\bf\dfrac{1}{x^{3}}$$\bf{{ - 3}}$$\bf{{(x - }}$$\bf\dfrac{1}{x})$

$\bf{{By \ Using \ Formula:-}}$

$\bf{{3^{3}}}$$\bf{{= x^{3} - }}$$\bf\dfrac{1}{x^{3}}$$\bf{{- 3}}$$\bf{{(3)}}$

$\implies \bf{{27}}$$\bf{{= x^{3} - }}$$\bf\dfrac{1}{x^{3}}$$\bf{{- 9}}$

$\implies \bf{{27 + 9}}$$\bf{{= x^{3} - }}$$\bf\dfrac{1}{x^{3}}$

$\implies \bf{{36}}$$\bf{{= x^{3} - }}$$\bf\dfrac{1}{x^{3}}$

$\therefore \bf{{ x^{3} - }}$$\bf\dfrac{1}{x^{3}}$$\bf{{= 36}}$

${\bf{\underline{\underline{Hence \ the \ correct \ option \ is \ (d) \ 36}}}}$

$\LARGE{\bf{\underline{\underline{Something \ More \ to \ Know :-}}}}$

$1)\bf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\2)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\3)\bf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})$