Question

Find the value of $x$ satisfying the equation $\frac{{36}^{\frac{7}{2}}-{36}^{\frac{9}{2}}}{{36}^{\frac{5}{2}}}=(x\times 126).$

Answer 1

$\frac{(36{)}^{\frac{7}{2}}-(36{)}^{\frac{9}{2}}}{(36{)}^{\frac{5}{2}}}=x\times 126$

$\Rightarrow \frac{(6^2{)}^{\frac{7}{2}}-(6^2{)}^{\frac{9}{2}}}{(6^2{)}^{\frac{5}{2}}}=21\times 6\times x$

$\Rightarrow \frac{6^7-6^9}{6^5}=21\times 6\times x$

$\Rightarrow \frac{6^5[6^2-6^4]}{6^5}=21\times 6\times x$

$\Rightarrow x=\frac{6^2-6^4}{21\times 6}$

$\Rightarrow x=\frac{36[1-6^2]}{21\times 6}$

$\Rightarrow x=\frac{2(1-6^2)}{7}=\frac{-70}{7}=-10$

$\therefore x=-10$