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If a ,b ,c ,d are positive real umbers s...

If `a ,b ,c ,d` are positive real umbers such that `a=b+c+d=2,t h e nM=(a+b)(c+d)` satisfies the relation `0lt=Mlt=1` `1lt=Mlt=2` `2lt=Mlt=3` `3lt=Mlt=4`

A

`0leMle1`

B

`1leMle2`

C

`2leMle3`

D

`3leMle4`

Text Solution

Verified by Experts

The correct Answer is:
A
Using `A.M.geG.M.,` we have
`((a+b)+(c+d))/(2)ge{(a+b)(c+d)}^(1//2)`
`implies" "(2)/(2)geM^((1)/(2))`
`implies" "Mle1`
As a, b, c, d`gt`0. Therefore, `M=(a+b)(c+d)gt0.`
Hence, `0leMle1.`
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