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AM,GM,HM Inequality

If a, b, c, d...

Question

If a,b,c,d are positive real numbers such that a+b+c+d = 2, then M = (a+b)(c+d) satisfies the relation

A

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B

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C

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D

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Solution

The correct option is A
$\frac{(a + b) + (c + d)}{2} \geq \sqrt{(a + b) (c + d)}$
or $\frac{2}{2} > \sqrt{M}$ or $1 \geq M$
Also $M > 0.$ So, $0 < M \leq 1.$

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