Question 67

If $$a-b=18$$ and $$a^3-b^3=324$$, then find ab.

Solution

Given, $$a-b=18$$ and

$$a^3-b^3=324$$

$$\Rightarrow$$ $$\left(a-b\right)\left(a^2+ab+b^2\right)=324$$

$$\Rightarrow$$ $$\left(18\right)\left(a^2-2ab+b^2+3ab\right)=324$$

$$\Rightarrow$$ $$\left(a-b\right)^2+3ab=18$$

$$\Rightarrow$$ $$\left(18\right)^2+3ab=18$$

$$\Rightarrow$$ $$324+3ab=18$$

$$\Rightarrow$$ $$3ab=-306$$

$$\Rightarrow$$ $$ab=-102$$

Hence, the correct answer is Option B

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