Question 55

If $$a^3+b^3=62$$ and a + b = 2, then the value of ab is:

Solution

Given, $$a+b=2$$

$$a^3+b^3=62$$

$$\Rightarrow$$ $$\left(a+b\right)\left(a^2-ab+b^2\right)=62$$

$$\Rightarrow$$ $$\left(2\right)\left(a^2+2ab+b^2-3ab\right)=62$$

$$\Rightarrow$$ $$\left(a+b\right)^2-3ab=31$$

$$\Rightarrow$$ $$\left(2\right)^2-3ab=31$$

$$\Rightarrow$$ $$4-3ab=31$$

$$\Rightarrow$$ $$3ab=-27$$

$$\Rightarrow$$ $$ab=-9$$

Hence, the correct answer is Option D

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