Question 74

If $$a + b = 27$$ and $$a^3 + b^3 = 5427$$, then find $$ab$$.

Solution

Given, $$a + b = 27$$

$$a^3 + b^3 = 5427$$

$$=$$> $$\left(a+b\right)\left(a^2+b^2-ab\right)=5427$$

$$=$$> $$27\left(a^2+b^2+2ab-3ab\right)=5427$$

$$=$$> $$\left(a+b\right)^2-3ab=201$$

$$=$$> $$\left(27\right)^2-3ab=201$$

$$=$$> $$729-3ab=201$$

$$=$$> $$3ab=729-201$$

$$=$$> $$3ab=528$$

$$=$$> $$ab=176$$

Hence, the correct answer is Option C

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