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 = 1So, 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 = $$\frac{1}{{\sqrt {27} }} = \frac{1}{{3\sqrt 3 }}$$
This Question Belongs to Arithmetic Ability >> Number System
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