Question

If (m/n)^3/8 + (n/m)^3/8 = 9 then find the value of (m/n)^3/4 + (n/m)^3/4.

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Answer 1

Answer:

$\ {( \frac{m}{n} )}^{ \frac{3}{8} } + {( \frac{n}{m} )}^{ \frac{3}{8} } = 9 \\ \\ squaring \: both \: side \\ \\ {[( { \frac{m}{n} )}^{ \frac{3}{8} } + {( \frac{n}{m} )}^{ \frac{3}{8} } ] }^{2} = {9}^{2} \\ \\ \\ {( \frac{m}{n} )}^{ \frac{3}{8} \times 2} + {( \frac{n}{m} )}^{ \frac{3}{8} \times 2} + 2 \times {( \frac{m}{n} )}^{ \frac{3}{8} } \times { (\frac{n}{m}) }^{ \frac{3}{8} } = 81 \\ \\ {( \frac{m}{n} )}^{ \frac{3}{4} } + {( \frac{n}{m}) }^{ \frac{3}{4} } + 2 \times {1}^{ \frac{3}{8} } = 81 \\ \\ \\ {( \frac{m}{n} )}^{ \frac{3}{4} } + {( \frac{n}{m}) }^{ \frac{3}{4} } + 2 = 81 \\ \\ \\{ \large{ \pink{ \boxed{ \sf{ {( \frac{m}{n} )}^{ \frac{3}{4} } + {( \frac{m}{n} )}^{ \frac{3}{4} } = 79}}}}}$

Answer 2

Answer:

79

Step-by-step explanation:

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