(x+y)*(x+z)*(y+z)>=8xyz How to show this, I suppose somehow with the AM–GM inequality, but don't know how. Thank you!
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Originally Posted by gotmejerry (x+y)*(x+z)*(y+z)>=8xyz How to show this, I suppose somehow with the AM–GM inequality, but don't know how. Thank you! Now multiply left hand sides and right hand sides of these three equations .
Thank you!
you are welcome
Just nitpicking... For x=1, y=-1, z=-1, you get: which is a contradiction.
Originally Posted by gotmejerry (x+y)*(x+z)*(y+z)>=8xyz How to show this, I suppose somehow with the AM–GM inequality, but don't know how. I assume that are non-negative. We have so . Expand . Do you see what to do next?
Sorry, I forgot that x,y,z are postives
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