Question

A/b + b/a = 1, then the value of a3 + b3will

Answer 1

$\frac{a}{b} + \frac{b }{a} = 1 \\ \\ \\ => \frac{ {a}^{2} + {b}^{2} }{ab} = 1 \\ \\ \\ = > {a}^{2} + {b}^{2} = ab$



Add 2ab on both sides,


=> a² + b² + 2ab = ab + 2ab

=> (a + b)² = 3ab

=> a + b = √3ab





Cube on both sides,


=> a³ + b³ + 3ab(a + b) = 3ab√3ab

=> a³ + b³ + 3ab√3ab = 3ab√3ab

=> a³ + b³ = 0