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If a2 + b2 + c2 = 1, what is the maximum value of abc ?
Answer & Solution
Correct 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 = $$\frac{1}{{\sqrt {27} }} = \frac{1}{{3\sqrt 3 }}$$
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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