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Question

If a, b, c, d are non-negative real numbers where a+b+c+d=1 , then the maximum value of ab+bc+cd+ad is

A
14
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B
3
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C
4
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D
none of these
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Solution

The correct option is B 14
ab+bc+cd+ad=(a+c)(b+d)
By the AM-GM inequality, (a+c)(b+d)(a+b+c+d2)2=14
The maximum value is 14

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