Find all functions defined on real numbers and taking real values such that
$ f(x)^{2}+2yf(x)+f(y)=f(y+f(x)) $
for all real numbers
Search found 217 matches
- Sun Sep 30, 2012 1:01 pm
- Forum: Algebra
- Topic: funEQUATION
- Replies: 5
- Views: 3527
- Tue Jul 24, 2012 8:33 pm
- Forum: Geometry
- Topic: Circumcenter on Euler line
- Replies: 2
- Views: 2029
Re: Circumcenter on Euler line
Hints: prove that $OX$ is the angle bisector of $YXZ$.so symmetrically $O$ is the incentre of triangle $XYZ$.$H$ is the incentre of $DEF$.$D$,$E$,$F$ are foot of altitudes of triangle $ABC$.prove that $XY$ is parallel to $DE$.symmetrically $XYZ$ and $DEF$ are homothetic.So $XD$,$YE$,$ZF$ and $OH$ ar...
- Mon May 28, 2012 7:27 pm
- Forum: International Mathematical Olympiad (IMO)
- Topic: ISL 2006
- Replies: 3
- Views: 3582
Re: ISL 2006
One can use similar quadrilaterals and ceva's theorem.
- Mon May 28, 2012 5:45 pm
- Forum: College / University Level
- Topic: Twin prime are infinite.
- Replies: 17
- Views: 19894
Re: Twin prine are infinite.
Saumitra Vai showed you sanzeed? well,how does the formula look like?
- Mon Apr 30, 2012 7:59 pm
- Forum: Geometry
- Topic: Trigonometry problem
- Replies: 2
- Views: 2250
Re: Trigonometry problem
yes,the problem posted in AoPS was solved assuming $A,B,C$ are angles of an acute triangle.
http://www.artofproblemsolving.com/Foru ... Inequality
http://www.artofproblemsolving.com/Foru ... Inequality
- Mon Apr 30, 2012 4:03 pm
- Forum: Geometry
- Topic: Trigonometry problem
- Replies: 2
- Views: 2250
Trigonometry problem
\[ \frac{\cos^{2}B\cos^{2}C}{\sin^{2}A}+\frac{\cos^{2}C\cos^{2}A}{\sin^{2}B}+\frac{\cos^{2}A\cos^{2}B}{\sin^{2}C}\le\frac{1}{4} \]
It's actually from mathlinks.To avoid latexing i used copy paste.
It's actually from mathlinks.To avoid latexing i used copy paste.
- Sun Apr 29, 2012 11:55 pm
- Forum: Geometry
- Topic: USAMO 2006-6
- Replies: 4
- Views: 3016
Re: USAMO 2006-6
Not so easily,Fahim vai.
- Sun Apr 29, 2012 8:40 pm
- Forum: Number Theory
- Topic: USAMO 2012-4
- Replies: 2
- Views: 2195
Re: USAMO 2012-4
nice problem.
- Sun Apr 29, 2012 3:32 pm
- Forum: Algebra
- Topic: You know what to do
- Replies: 1
- Views: 1813
You know what to do
For every positive integer $n$ ,prove that
\[\sum_{k=0}^{n-1}(-1)^k cos ^n (\frac{k\pi }{n})=\frac{n}{2^{n-1}}\]
\[\sum_{k=0}^{n-1}(-1)^k cos ^n (\frac{k\pi }{n})=\frac{n}{2^{n-1}}\]
- Thu Apr 26, 2012 11:50 pm
- Forum: Number Theory
- Topic: A problem (or exercise may be)
- Replies: 12
- Views: 6304
Re: A problem (or exercise may be)
adib,how do you claim that together your hints establish mahi's solution?$a^x-1=(a-1)^x$ is satisfied only by $x=1$.