Question 116

if $$\frac{a}{b} + \frac{b}{a} - 1$$ = 0, then the value of $$a^3 + b^3$$ is

Solution

Expression : $$\frac{a}{b} + \frac{b}{a} - 1 = 0$$

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

=> $$a^2 + b^2 = ab$$ ----------Eqn(1)

To find : $$a^3 + b^3$$

= $$(a + b) (a^2 + b^2 - ab)$$

Using eqn(1), we get :

= $$(a + b) (ab - ab)$$

= 0

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