Question

विस्तार करा: $\bigg \lgroup \frac{5x}{y}+\frac{y}{5x} \bigg \rgroup^3$

Answer 1

विस्तार करा: $\bigg \lgroup \frac{5x}{y}+\frac{y}{5x} \bigg \rgroup^3$

विस्तार सूत्र:

${(a+b)}^{3} = {a}^{3} + {b}^{3} + 3 {a}^{2} b + 3a {b}^{2} \\ \\ a=\frac{5x}{y}\\ \\ b=\frac{y}{5x} \\ \\ \bigg \lgroup \frac{5x}{y}+\frac{y}{5x} \bigg \rgroup^3 = {\bigg(\frac{5x}{y}\bigg)}^{3} + {\bigg(\frac{y}{5x}}\bigg)^{3} + \\\\\\3 {\bigg(\frac{5x}{y}\bigg)}^{2} \bigg(\frac{y}{5x}\bigg)+ 3\bigg(\frac{5x}{y}\bigg) {\bigg(\frac{y}{5x}\bigg)}^{2} \\ \\ = \frac{125x^{3}}{y^{3}}+ \frac{y^{3}}{125x^{3}} + \frac{15x}{y}+ \frac{3y}{5x}$

विस्तार:
$\\ \bigg \lgroup \frac{5x}{y}+\frac{y}{5x} \bigg \rgroup^3 = \frac{125x^{3}}{y^{3}}+ \frac{y^{3}}{125x^{3}} + \frac{15x}{y}+ \frac{3y}{5x}$