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![[Post New]](/templates/default/images/icon_minipost_new.gif) 2 Nov 2007 22:13:08 IST
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Q . prove that (ab+xy)(ax+by)>4abxy.
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Using AM, GM inequality,
( ab + xy) / 2 > rt( abxy) . .....(1)
( ax + by) / 2 > rt ( abxy) .......(2)
multiply (1) and (2)
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3 Nov 2007 20:46:10 IST
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(ab + xy)/2 > (abxy)^1/2
(ax + by)/2 > (abxy)^1/2
so
(ab+xy)(ax+by)/4 > abxy
or, (ab+xy)(ax+by) > 4abxy
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