Question

$if \: \frac{a}{b} + \frac{b}{a} = 1 \\ {a}^{3} + {b}^{3} = ??? \\ dont \: spam \\ want \: the \: answer \: with \: all \: the \: steps.$

Answer 1

Given =>>> a/b + b/a = 1

           (a^2 + b^2)/ab = 1.

          a^2 + b^2 = ab   --- (1)

Then a^3 + b^3 = (a + b)(a^2 + b^2 - ab)

                      = (a + b)(ab - ab)  (From (1))

                          = 0

Answer 2

Solution

$\frac{a}{b}+\frac{b}{a}=1\\ \frac{a^{2}+b^{2}}{ab}=1\\ a^{2}+b^{2} =ab$  $a^{3}+b^{3} = (a+b)(a^{2} -ab+b^{2})\\ (a+b)(ab-ab)\\ (a+b)(0)\\ 0$  

Answer is 0  

Hence Proved