Question 57

If $$a^3 - b^3 = 899 and a - b = 31$$, then $$(a - b)^2 + 3ab$$ is equal to:

Solution

Given, $$a^3-b^3=899$$ and $$a-b=31$$

$$=$$> $$\left(a-b\right)\left(a^2+ab+b^2\right)=899$$

$$=$$> $$31\left(a^2+ab+b^2-2ab+2ab\right)=899$$

$$=$$> $$\left(a-b\right)^2+3ab=\frac{899}{31}$$

$$=$$> $$\left(a-b\right)^2+3ab=29$$

Hence, the correct answer is Option D

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