Question
If $$a = \frac{{{b^2}}}{{b - a}}{\text{,}}$$ then the value of a3 + b3 is?
Answer: Option B
$$\eqalign{
& a = \frac{{{b^2}}}{{b - a}} \cr
& \Rightarrow a\left( {b - a} \right) = {b^2} \cr
& \Rightarrow ab - {a^2} = {b^2} \cr
& \Rightarrow {a^2} + {b^2} - ab = 0 \cr
& \Rightarrow {a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} + {b^2} - ab} \right) \cr
& \Rightarrow {a^3} + {b^3} = 0 \cr} $$
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$$\eqalign{
& a = \frac{{{b^2}}}{{b - a}} \cr
& \Rightarrow a\left( {b - a} \right) = {b^2} \cr
& \Rightarrow ab - {a^2} = {b^2} \cr
& \Rightarrow {a^2} + {b^2} - ab = 0 \cr
& \Rightarrow {a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} + {b^2} - ab} \right) \cr
& \Rightarrow {a^3} + {b^3} = 0 \cr} $$
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