Question 56

If $$a^3 + b^3 = 1344 and a + b = 28$$, then $$(a + b)^2 - 3ab$$ is equal to:

Solution

Given, $$a^3+b^3=1344$$ and $$a+b=28$$

$$=$$> $$\left(a+b\right)\left(a^2-ab+b^2\right)=1344$$

$$=$$> $$28\left(a^2-ab+b^2-2ab+2ab\right)=1344$$

$$=$$> $$\left(a+b\right)^2-3ab=\frac{1344}{28}$$

$$=$$> $$\left(a+b\right)^2-3ab=48$$

Hence, the correct answer is Option A

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