Question 71

If a + b = 8 and ab = 12, then the value of $$a^3 + b^3$$ is:

Solution

Given, $$a+b=8$$ and $$ab=12$$

$$=$$> $$\left(a+b\right)^3=8^3$$

$$=$$> $$a^3+b^3+3ab\left(a+b\right)=512$$

$$=$$> $$a^3+b^3+3\left(12\right)\left(8\right)=512$$

$$=$$> $$a^3+b^3+288=512$$

$$=$$> $$a^3+b^3=512-288$$

$$=$$> $$a^3+b^3=224$$

Hence, the correct answer is Option B

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