Question
If $$\frac{a}{b} + \frac{b}{a} = 1{\text{,}}$$ then the value of a3 + b3 will be?
Answer: Option B
$$\eqalign{
& {a^2} + {b^2} = ab\,........(i) \cr
& {a^2} + {b^2} - ab = 0 \cr
& \because {a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} + {b^2} - ab} \right)\,.....(ii) \cr
& {\text{From equation (i) and (ii)}} \cr
& \Rightarrow {a^3} + {b^3} = \left( {a + b} \right)\left( 0 \right) \cr
& \Rightarrow {a^3} + {b^3} = 0 \cr} $$
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$$\eqalign{
& {a^2} + {b^2} = ab\,........(i) \cr
& {a^2} + {b^2} - ab = 0 \cr
& \because {a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} + {b^2} - ab} \right)\,.....(ii) \cr
& {\text{From equation (i) and (ii)}} \cr
& \Rightarrow {a^3} + {b^3} = \left( {a + b} \right)\left( 0 \right) \cr
& \Rightarrow {a^3} + {b^3} = 0 \cr} $$
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