If a² + b² + c² = 1, what is the maximum value of abc ?

A. $$\frac{1}{3}$$

B. $$\frac{1}{3{\sqrt 3 }}$$

C. $$\frac{2}{{\sqrt 3 }}$$

D. 1

Answer: Option B

Solution(By Examveda Team)

a² + b² + c² = 1
So, the maximum value of a² b² c² = $$\frac{1}{3}$$ × $$\frac{1}{3}$$ × $$\frac{1}{3}$$ = $$\frac{1}{27}$$
(∵ when sum of three positive quantities is fixed, the product will be maximum when the quantities are equal)
Hence, maximum value of abc = $$\frac{1}{{\sqrt {27} }} = \frac{1}{{3\sqrt 3 }}$$