Question

विस्तार करा: $\bigg \lgroup \frac{x}{3} -\frac{3}{x} \bigg \rgroup^3$

Answer 1

विस्तार सूत्र:

$( {a - b)}^{3} = {a}^{3} - {b}^{3} - 3 {a}^{2} b + 3a {b}^{2}$
विस्तार करा: $\bigg \lgroup \frac{x}{3} -\frac{3}{x} \bigg \rgroup^3$

$a = \frac{x}{3} \\ \\ b = \frac{3}{x}$
$\bigg( { \frac{x}{3} - \frac{3}{x} \bigg)}^{3} = \bigg({ \frac{x}{3} \bigg)}^{3} - \bigg({ \frac{3}{x} \bigg)}^{3} - 3 \bigg({ \frac{x}{3}\bigg)}^{2} \bigg( \frac{3}{x}\bigg) + 3\bigg( \frac{x}{3}\bigg) {\bigg( \frac{3}{x}\bigg) }^{2} \\ \\ = \frac{ {x}^{3} }{27} - \frac{27}{ {x}^{3} } - x + \frac{9}{x}$
विस्तार:

$\bigg \lgroup \frac{x}{3} -\frac{3}{x} \bigg \rgroup^3 =\frac{ {x}^{3} }{27} - \frac{27}{ {x}^{3} } - x + \frac{9}{x}$