If a2 + b2 + c2 = 1, what is the maximum value of abc ?
Options:
A . $$\frac{1}{3}$$
B . $$\frac{1}{3{\sqrt 3 }}$$
C . $$\frac{2}{{\sqrt 3 }}$$
D . 1
Answer: Option B 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 = $$\frac{1}{{\sqrt {27} }} = \frac{1}{{3\sqrt 3 }}$$
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