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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