AM-GM-HM on expression with parameters?

Asked Jul 06 '14 at 15:22

Active Jul 06 '14 at 15:39

Viewed 60 times

This question, which I believe is easier to answer, is related to my previous question: Finding a value that makes an expression negative

I am persistent - and need some ideas to help me prove something.

How can I show that:

$$W^2X-A(AW-X)^3<\frac{(AW-X)^4}{C}$$

where $$A,C,W,X>0$$

and $$AW>X?$$

Should I proceed by adding $A(AW-X)^3$ to both sides, and then applying AM-GM-HM? Or what other inequalities would be useful here? I'm new to Holder's, Jensen's, etc.

If you'd like, I have made the above expression into:

$$P-QR^3<\frac{R^4}{C}$$

Thanks for any help!

edited Apr 13 '17 at 12:21

Community

asked Jul 06 '14 at 15:22

If $W=10, A=1/5, X=1,C=10$... – chubakueno Jul 06 '14 at 15:49
I tried many times and several ways, cannot!! please check – Mohammad W. Alomari Jul 06 '14 at 15:55
@mwomath The inequality is false. – chubakueno Jul 06 '14 at 16:09
@chubakueno You are right. Would you mind if I scrap this question and start a new one, one with more context and details? Thanks. – Jul 06 '14 at 16:18
I think not, because radically editing the question would be more counter productive than starting a new one :) – chubakueno Jul 06 '14 at 16:26
@chubakueno Ok. I have started this new question then: http://math.stackexchange.com/questions/858089/inequality-involving-fractions-and-several-variables – Jul 06 '14 at 16:33
Uhmm... there is something I don't understand. Is your question ill -posed, or it was right? If it is the second, you may answer yourself to close the thread. – chubakueno Jul 06 '14 at 16:38
@chubakueno I believe this AM-GM-HM on expression with parameters question was ill-posed... – Jul 06 '14 at 16:40

AM-GM-HM on expression with parameters?

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