Question

State whether the statement is True or False:

The square of $(\frac{5a}{6b}+\frac{6b}{5a})$ is equal to $\frac{25a^2}{36b^2}-2+\frac{36b^2}{25a^2}$.

• A. True
• B. False

Answer 1

The correct option is B False

Given, square of $(\frac{5a}{6b}+\frac{6b}{5a})$ ,

i.e. $(\frac{5a}{6b}+\frac{6b}{5a}{)}^2$.

Applying the formula $(a+b{)}^2=a^2+2ab+b^2$.

$(\frac{5a}{6b}+\frac{6b}{5a}{)}^2$

$=(\frac{5a}{6b}{)}^2+2(\frac{5a}{6b}\left)\right(\frac{6b}{5a})+(\frac{6b}{5a}{)}^2$

$=\left(\frac{25a^2}{36b^2}\right)+2+\left(\frac{36b^2}{25a^2}\right)$

$=\frac{25a^2}{36b^2}+2+\frac{36b^2}{25a^2}$.

Hence, the statement is false.

Therefore, option $B$ is correct.