## Search found 63 matches

Wed Jun 27, 2018 8:14 pm
Forum: Social Lounge
Topic: short query
Replies: 9
Views: 1665

### Re: short query

Mon Apr 23, 2018 9:59 pm
Forum: Algebra
Topic: FE from USAMO 2002
Replies: 4
Views: 939

### Re: FE from USAMO 2002

The fact that $f(x^2)=xf(x)$ implies that $f(x^2-y^2)=f(x^2)-f(y^2)$ so it implies that $f(a-b)=f(a)-f(b)$ for $a$ and $b$ positive perfect square; why do you say that this expression is true also for $a$ and $b$ positive numbers (and so no necessary positive perfect squares...)? And why after do y...
Sat Apr 21, 2018 11:25 pm
Forum: Algebra
Topic: Inequality with a,b,c sides of a triangle
Replies: 7
Views: 1745

### Re: Inequality with a,b,c sides of a triangle

Katy729 wrote:
Sat Apr 21, 2018 10:53 pm
Yes, now understand. Very gentle Atonu! Okay, you can check this out if you have confusion about the proof of negative exponent.
Sat Apr 21, 2018 10:36 pm
Forum: Algebra
Topic: Inequality with a,b,c sides of a triangle
Replies: 7
Views: 1745

### Re: Inequality with a,b,c sides of a triangle

Thanks Atonu, now is clear! :) Only a doubt, can you put a link where is wrote the property that you say? Because I found that the exponent ($n$) must be positive, yes in your cases the numbers are positive but where is wrote? I saw here but I didn't find the property that you say... :( https://en....
Sat Apr 21, 2018 9:45 pm
Forum: Algebra
Topic: Inequality with a,b,c sides of a triangle
Replies: 7
Views: 1745

### Re: Inequality with a,b,c sides of a triangle

Sorry Atonu, but I don't understand some passages... :( Why exactly $\sum_{cyc} \frac{\sqrt{b+c-a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}= \sum_{cyc} \sqrt{1- \frac{(x-y)(x-z)}{2x^2}} \le \sum_{cyc} (1-\frac{(x-y)(x-z)}{4x^2}) = 3 - \frac{1}{4} \sum_{cyc} x^{-2}(x-y)(x-z)$ ? And how do you use exactly Sh...
Fri Apr 20, 2018 9:59 pm
Forum: Secondary Level
Topic: Easy Projective Geo
Replies: 3
Views: 1126

### Re: Easy Projective Geo

Harmonic quad approach is quite intuitive. Anyone tried bash?
Btw, apart from projective I solved it by cartesian coordinates. I don't have enough patience to type that lengthy and annoying solution here.
Fri Apr 20, 2018 12:20 pm
Forum: Geometry
Topic: EGMO 2018 P5
Replies: 3
Views: 1138

### Re: EGMO 2018 P5

Okay, I copied it from my aops post. Let $X$ be the midpoint of the arc $AB$ not containing $C$. Also let $Y$ and $Z$ be the tangency point of $\Omega$ with $AB$ and $\Gamma$ respectively. $D$ is the feet of angle bisector of $\angle ACB$. $I$ denotes the incenter of $\triangle ABC$ Lemma 1: $X,Y,Z$...
Sat Apr 14, 2018 8:21 pm
Forum: Number Theory
Topic: 2018 BDMO NT exam P4
Replies: 2
Views: 890