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

Share on Whatsapp Share on Whatsapp

Create a FREE account and get: