Question

Answer is option (A) Pls give correct explanation of this answer​

Answer 1

${ (\frac{m}{n} )}^{ \frac{3}{8} } + { (\frac{n}{m} )}^{ \frac{3}{8} } = 9 \\ \: let \: \frac{m}{n } = x \: and \: \frac{n}{m} = y \\ {x}^{ \frac{3}{8} } + {y}^{ \frac{3}{8} } = 9 \\ squaring \: on \: both \: sides \: \\({x}^{ \frac{3}{8} } + {y}^{ \frac{3}{8} } )^{2} = {9}^{2} \\ ({x}^{ \frac{3}{8} } )^{2} + ( {y}^{ \frac{3}{8} })^{2} + 2({x}^{ \frac{3}{8} } ) ( {y}^{ \frac{3}{8} }) = {9}^{2} \\ {x}^{ \frac{6}{8} } + {y}^{ \frac{6}{8} } + 2(xy) ^{ \frac{3}{8} } = 81 \\ ({\frac{m}{n} })^{ \frac{6}{8} } + ({\frac{n}{m} })^{ \frac{6}{8} } + 2( { \frac{mn}{nm} })^{ \frac{3}{8} } = 81 \\ ({\frac{m}{n} })^{ \frac{3}{4} } + ({\frac{n}{m} })^{ \frac{3}{4} } + 2( {1})^{ \frac{3}{8} } = 81 \\ ({\frac{m}{n} })^{ \frac{3}{4} } + ({\frac{n}{m} })^{ \frac{3}{4} } + 2 (1) = 81 \\ ({\frac{m}{n} })^{ \frac{3}{4} } + ({\frac{n}{m} })^{ \frac{3}{4} } = 81 - 2 \\ ({\frac{m}{n} })^{ \frac{3}{4} } + ({\frac{n}{m} })^{ \frac{3}{4} } = 79$