this is bugging me:
for any \( a, b, c, d > 0\) prove that
\[ {a^2 \over b} + {b^2 \over c} + {c^2 \over d} +{d^2 \over a} \geq a+ b+c+d \]
Also if \( a+b+c=ab+bc+ca \)
\[ \frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a} \geq {(a + b +c)(a^2 + b^2 + c^2)\over ab + bc +ac} \]

- experimentX

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- anonymous

man u most be on tensor and pde now...lol :)

- experimentX

on ... just for fun. if possible quick ... man

- experimentX

just this is bugging me so badly
Exercise 1.1.8.

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## More answers

- experimentX

https://web.williams.edu/go/math/sjmiller/public_html/161/articles/Riasat_BasicsOlympiadInequalities.pdf

- experimentX

Ctrl + F ... search 1.1.8.
Don't have much time to waste

- anonymous

Actually, this question is very easy.. @experimentX

- experimentX

how ??

- anonymous

Did not you get the question clearly ??
It is saying to prove that thing..

- experimentX

how do you prove that?

- anonymous

Actually, I am talking about question..
Its solution is easy or not I don't know..
Ha ha ha..

- experimentX

already wasted 1 hrs ... can't waste another ... lol

- anonymous

Actually, that pdf is quite useful for me..
Thanks for giving me that..

- experimentX

some fool upvoted me :D ... that doesn't work at all .... lol

- anonymous

man second one's RHS will simplify to\[a^2+b^2+c^2\]

- experimentX

yeah ... i know that ... just need to prove it.

- experimentX

olypiad problems ... i find it extremely difficult even at my level man!! i need to dig a hole hide.

- experimentX

what kind of technique is this
http://www.wolframalpha.com/input/?i=Minimize[{x+%2B+2+n%2Fx%2C+n+%3C%3D+3+%26%26+x+%3E%3D+3}%2C+{x}]

- anonymous

for the first one use AM_GM 4 times\[\frac{a^2}{b}+b\ge 2a\]\[\frac{b^2}{c}+c\ge 2b\]...

- experimentX

crazy crafty manipulation

- experimentX

the second one ... i can prove half of the original problem without it.

- experimentX

the last inequality i can get bu the use of quadratic formula ... but can't find any use of ... inequality n<=3

- experimentX

particularly I mean this
http://www.wolframalpha.com/input/?i=Minimize[{x+%2B+3+n%2Fx%2C++x+%3E%3D+3}%2C+{x}]

- experimentX

what kind of problems is this
x + 3n/x ... for x >= 3

- anonymous

sorry man i was out...how u realte this to second one?

- experimentX

can't ...have to do without it.

- experimentX

don't know what property is used here ..

- anonymous

i found it from one my books i will copy it here
\[(a+b+c)(\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}) \geq (a+b+c)(a^2+b^2+c^2)\]\[\frac{ab^3}{c}+\frac{bc^3}{a}+\frac{ca^3}{b} \geq b^2c+c^2a+a^2b\]use AM_GM 3 times\[\frac{ab^{3}}{c}+\frac{bc^{3}}{a}\ge 2b^{2}c\]...

- experimentX

which book do you use man??

- anonymous

oh sorry man original book is in persian and not translated to other languages :(

- anonymous

this is 500 pages about geometry and inequalities

- experimentX

you follow a very good writer!!

- anonymous

yeah :)

- anonymous

see u later santosh

- experimentX

see ya :) thanks for help man

- anonymous

Are you Linkha Santosh @experimentX ?? Sorry if there is any spelling mistake in name..

- experimentX

no mistake ... the first is my surname.

- anonymous

Santosh Linkha ..??

- anonymous

That day you said now a days, everyone is on Facebook and I was just wondering why experimentX who said those words is not on Facebook..??
Now, it is clear to me..

- experimentX

lol ... what words?

- anonymous

I have written those..
"Everyone is on Facebook"..
I think these you said to Yahoo that day..

- experimentX

oh yeah ... kinda remembered on thing
"if you are searched in Google instead of fB then you are successful person"

- anonymous

Ha ha ha...
Yeah, this is true one..

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