• # question_answer The third proportional between $({{a}^{2}}-{{b}^{2}})$ and $({{a}^{2}}+{{b}^{2}})$ is A)  $\frac{a+b}{a-b}$      B)  $\frac{a-b}{a+b}$C)  $\frac{{{(a-b)}^{2}}}{a+b}$ D)  $\frac{{{(a+b)}^{3}}}{a-b}$

[d] Let x be the required third proportional $\therefore$ $\frac{{{a}^{2}}-{{b}^{2}}}{{{(a+b)}^{2}}}=\frac{{{(a+b)}^{2}}}{x}$ $\Rightarrow$ $x=\frac{{{(a+b)}^{4}}}{{{a}^{2}}-{{b}^{2}}}=\frac{{{(a+b)}^{3}}(a+b)}{(a+b)(a-b)}=\frac{{{(a+b)}^{3}}}{(a-b)}$