Question

If ${\left(\frac{m}{n}\right)}^{\frac{3}{8}}+{\left(\frac{n}{m}\right)}^{\frac{3}{8}}=9$ then find the value of ${\left(\frac{m}{n}\right)}^{\frac{3}{4}}+{\left(\frac{n}{m}\right)}^{\frac{3}{4}}$

• A. $79$
• B. $72$
• C. $83$
• D. $84$

Answer 1

The correct option is A $79$

$(\frac{m}{n}{)}^{\frac{3}{8}}+(\frac{n}{m}{)}^{\frac{3}{8}}=9$

$\left[\right(\frac{m}{n}{)}^{\frac{3}{8}}+(\frac{n}{m}{)}^{\frac{3}{8}}{]}^2=9^2$

$\left(\right(\frac{m}{n}{)}^{\frac{3}{8}}{)}^2+\left(\right(\frac{n}{m}{)}^{\frac{3}{8}}{)}^2+2\left(\right(\frac{m}{n}{)}^{\frac{3}{8}}\left)\right(\left(\frac{n}{m}{)}^{\frac{3}{8}}\right)=81$

$(\frac{m}{n}{)}^{\frac{3}{4}}+(\frac{n}{m}{)}^{\frac{3}{4}}=81-2=79$