## Search found 21 matches

Tue Dec 27, 2011 12:53 am
Topic: BdMO National Higher Secondary 2009/5
Replies: 5
Views: 2206

### Re: BdMO National Higher Secondary 2009/5

let$O_{1}=$circumcenter of $\triangle AMC$$X=O_{1}P\cap AB,Y=BA\cap CO_{1}$$O_{1}AXM$is a rhombus. $\Rightarrow AE=EM\Rightarrow AP=PM\Rightarrow \angle PYA=\angle PCA=\angle PAM=\angle PCM$
Thu Dec 15, 2011 9:10 pm
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2007
Replies: 5
Views: 2935

### APMO 2007

Given $\sqrt{x}+\sqrt{y}+\sqrt{z}=1$ for all positive real $x,y,z$Prove $\frac{x^2+yz}{\sqrt{2x^2(y+z)}} + \frac{y^2+zx}{\sqrt{2y^2(z+x)}} + \frac{z^2+xy}{\sqrt{2z^2(x+y)}} \geq1$
Sun Nov 13, 2011 4:04 pm
Forum: Number Theory
Topic: IMO LONGLISTED PROBLEM 1974
Replies: 1
Views: 1060

### Re: IMO LONGLISTED PROBLEM 1974

we've to prove $2^{147}=1(mod 343)$
we know $2^{9}=169(mod343)\Rightarrow 2^{144}=43(mod343)$
and $2^{3}=351(mod343)$
multiplying both this we get the desired result.
Tue Nov 08, 2011 9:14 pm
Forum: Algebra
Replies: 0
Views: 912

could somebody please explain me why a discriminant has to be negative for a quadratic function to be positive?? when a quadratic function is positive, does it refer that it's value is positive or the signs are all positive??
Tue Nov 08, 2011 11:55 am
Forum: Physics
Topic: রিলেটিবিটি
Replies: 8
Views: 3092

### Re: রিলেটিবিটি

I think so. Cuz the speed of light is absolute irrespective of all spectators and objects of arbitrary speed.
Mon Nov 07, 2011 9:17 pm
Topic: Problems Involving Triangles
Replies: 8
Views: 2725

### Re: Problems Involving Triangles

number 3. $AP,BP,CP$ are concurrent at $P$
By definition, Reflection of P across the midpoint of BC lies on AP. So all those reflective lines are concurrent at P. Mon Nov 07, 2011 9:07 pm
Topic: Problems Involving Triangles
Replies: 8
Views: 2725

### Re: Problems Involving Triangles

Number 2. $13/2,5$
@tiham, rookie mistake Mon Nov 07, 2011 1:03 pm
Forum: National Math Camp
Topic: Exercise-1.15(new book) (BOMC-2011)
Replies: 10
Views: 3910

### Re: Exercise-1.15(new book) (BOMC-2011)

could somebody please explain me why a discriminant has to be negative for a quadratic function to be positive?? when a quadratic function is positive, does it refer that it's value is positive or the signs are all positive??
Mon Nov 07, 2011 6:42 am
Forum: National Math Camp
Topic: Exercise-1.14(new book) (BOMC-2011)
Replies: 16
Views: 4991

### Re: Exercise-1.14(new book) (BOMC-2011)

$\left \lfloor \sqrt{\left ( 4n^2+n \right )} \right \rfloor=2n$
which leads us to $n< \left ( n+\left ( 1/16 \right ) \right )$and its obvious. Mon Nov 07, 2011 6:35 am
Forum: National Math Camp
Topic: Exercise-1.15(new book) (BOMC-2011)
Replies: 10
Views: 3910

### Re: Exercise-1.15(new book) (BOMC-2011)

oww. so silly of me. abc=1 condition was missed by me. Now i understand sourov's approach. Bt is my process right??