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Sum of n Terms

If a, b, c ar...

Question

If a, b, c are positive real numbers such that a + b + c = 1 then the least value of $\frac{(1 + a) (1 + b) (1 + c)}{(1 - a) (1 - b) (1 - c)} i s$ is

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Solution

The correct option is B
8

a = 1 - b - c

$\Rightarrow 1 + a = (1 - b) + (1 - c) \geq 2 \sqrt{(1 - b) (1 - c)} ∴ (1 + a) (1 + b) (1 + c) \geq 8 (1 - a) (1 - b) (1 - c)$

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