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Question

# If a1,a2,a3,a4,a5>0 thena1a2+a3+a2a3+a4+a3a4+a5+a4a5+a1+a5a1+a2≥52

A
Is true
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B
Is false
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C
Is True only for some values of an
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D
Nothing can be said for sure
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Solution

## The correct option is A Is trueIf we write, the expression asa21a1a2+a1a3+a22a2a3+a2a4+a23a3a4+a3a5+a24a4a5+a4a1+a25a5a1+a5a2Which we know is, ≥(a1+a2+a3+a4+a5)2∑alamNow, we have(a1+a2+a3+a4+a5)2=∑(a2n)+2(alam)If the condition in option (A) was True, then2(a21+a22+a23+a24+a25)+4∑alam≥5∑alamwhich reduces to ∑(al−am)2≥0Thus option (A) itself is correct.

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