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Prove that (a b+x y)(a x+b y)>4a b x y(a...

Prove that `(a b+x y)(a x+b y)>4a b x y(a , b ,x ,y >0)dot`

Text Solution

Verified by Experts

Using A.M `ge` G.M we have
`(ab + xy)/(2) gt sqrt(abxy)`
`implies ax + xy gt 2 sqrt(abxy)`
similarly, ax + by `gt 2 sqrt(abxy)`
Multiplying (1) and (2) we get
`(ab + xy) (ax + by) gt 4abxy`
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