Question 72
If a and b are two positive real numbers such that a + b = 20 and ab = 4, then the value of $$a^3 + b^3$$ is:
Solution
Given, $$a+b=20$$ and $$ab=4$$
$$=$$> $$\left(a+b\right)^3=20^3$$
$$=$$> $$a^3+b^3+3ab\left(a+b\right)=8000$$
$$=$$> $$a^3+b^3+3\left(4\right)\left(20\right)=8000$$
$$=$$> $$a^3+b^3+240=8000$$
$$=$$> $$a^3+b^3=8000-240$$
$$=$$> $$a^3+b^3=7760$$
Hence, the correct answer is Option A
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