Question

a/b +b/a=3,, then a^3/b^3+b^3/a^3=?​

Answer 1

SOLUTION :

$\sf \frac{a}{b} + \frac{b}{a} = 3$

$\sf \implies \: {( \frac{a}{b} + \frac{b}{a}) }^{3} = 27$

$\sf \implies \: {( \frac{a}{b} )}^{3} + {( \frac{b}{a} )}^{3} + 3 \times \frac{a}{b} \times \frac{b}{a} ( \frac{a}{b} + \frac{b}{a} ) = 27$

$\sf \implies \: {( \frac{a}{b}) }^{3} + { (\frac{b}{a}) }^{3} + 3( \frac{a}{b} + \frac{b}{a} ) = 27$

$\sf \implies {( \frac{a}{b} )}^{3} + {( \frac{b}{a}) }^{3} = 27 - 3 \times 3 \: \: \: \: [putting \: value \: of \: ( \frac{a}{b} + \frac{b}{a} ) ]$

$\sf \implies \boxed{ \mathfrak {{( \frac{a}{b} )}^{3} + {( \frac{b}{a}) }^{3} = 18}}$