Find the square of 5 a 6 b -6 b 5 a - Vidyadip

Question

Find the square of $\frac{5 a}{6 b}-\frac{6 b}{5 a}$

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Answer

$ \left(\frac{5 \mathrm{a}}{6 \mathrm{~b}}-\frac{6 \mathrm{~b}}{5 \mathrm{a}}\right)^2$
$=\left(\frac{5 \mathrm{a}}{6 \mathrm{~b}}\right)^2+\left(\frac{6 \mathrm{~b}}{5 \mathrm{a}}\right)^2-2 \times \frac{5 \mathrm{a}}{6 \mathrm{~b}} \times \frac{6 \mathrm{~b}}{5 \mathrm{a}}$
$ =\frac{25 \mathrm{a}^2}{36 \mathrm{a}^2}-2+\frac{36 \mathrm{~b}^3}{25 \mathrm{a}^2}$

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