Question

please answer it fast

(a/b)^3+(b/a)^3​

Answer 1

Question given :

• Simplify : $\sf\dfrac{a}{b}^3\:+\:\dfrac{b}{a}^3$

Given :

• $\sf\dfrac{a}{b}^3\:+\:\dfrac{b}{a}^3$

Identity used :

• a³ + b³ = ( a + b )( a² + b² - ab )

Solution required :

By using the identity a³ + b³ = ( a + b )( a² + b² - ab )

We get ,

= $\sf\dfrac{a}{b}^3\:+\:\dfrac{b}{a}^3$

= $\sf\:(\dfrac{a}{b}\:+\:\dfrac{b}{a})(\dfrac{a}{b}^2\:+\:\dfrac{b}{a}^2\:-\:\dfrac{a}{b}\:\times\:\dfrac{b}{a})$

= $\sf\:(\dfrac{a}{b}\:+\:\dfrac{b}{a})(\dfrac{a^2}{b^2}\:+\:\dfrac{b^2}{a^2}\:-\:\dfrac{ab}{ba})$