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# A nice inequalities question. Watch

1. Show that, if p>m>0 then
p-m/p+m < x^2-2mx +p^2/x^2 +2mx+p^2<p+m/p-m
for all real values of x
feel free to post solutions and discuss.
The signs are less then and equal to but i didnt know how to write them using my phone.
2. taken from c j bradleys book on inequalities.

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3. (Original post by physicsmaths)
Show that, if p>m>0 then
p-m/p+m < x^2-2mx +p^2/x^2 +2mx+p^2<p+m/p-m
for all real values of x
feel free to post solutions and discuss.
The signs are less then and equal to but i didnt know how to write them using my phone.
4. (Original post by TenOfThem)
Thanks alot bro!

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5. (Original post by TenOfThem)
This seems to work out fairly easily via a calculus approach. (Optimise the function in the middle - the upper and lower bounds seem to be as good as possible).

Are they looking more for an "inequality manipulation" type of solution?
6. (Original post by atsruser)

Are they looking more for an "inequality manipulation" type of solution?
No idea, I am not the OP
7. (Original post by atsruser)
This seems to work out fairly easily via a calculus approach. (Optimise the function in the middle - the upper and lower bounds seem to be as good as possible).

Are they looking more for an "inequality manipulatiown" type of solution?
i know the answer, this is just for others. Yep its a show that not a proof. A hint is they want some factorisation, ideally difference of squares.

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