Question : If $(a-b)=9$, and $(a^3-b^3)$ = 4401, find the value of $ab$.
Option 1: 190
Option 2: 112
Option 3: 162
Option 4: 136
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Correct Answer: 136
Solution :
Given: $(a-b)=9$ and $\left(a^3-b^3\right)=4401$
Taking, $(a-b)=9$
Cubing both sides, we get,
$⇒a^3-b^3-3ab(a-b)=729$
$⇒4401-3ab(9)=729$
$⇒27ab=4401-729$
$⇒ab=\frac{3672}{27}=136$
Hence, the correct answer is 136.
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