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If a,b,c,d are positive real number with...

If a,b,c,d are positive real number with `a + b + c + d=2` ,then `M =(a+b)(c+d)` satisfies the inequality

A

`0 lt M le 1`

B

`1 le M le 2`

C

`2 le M le 3`

D

`3 le M le 4`

Text Solution

Verified by Experts

The correct Answer is:
A
Since, `AM ge GM`, then
`((a +b) + (c +d))/(2) ge sqrt((a + b) (c +d)) rArr M le 1`
Also, `(a + b) + (c +d) gt 0 " " [ :' a, b, c, d, gt0]`
`:. 0 lt M le 1`
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