Search found 21 matches

by Ashfaq Uday
Tue Dec 27, 2011 12:53 am
Forum: National Math Olympiad (BdMO)
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. \[\Rightarrow AE=EM\Rightarrow AP=PM\Rightarrow \angle PYA=\angle PCA=\angle PAM=\angle PCM\]
by Ashfaq Uday
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 \[\frac{x^2+yz}{\sqrt{2x^2(y+z)}} + \frac{y^2+zx}{\sqrt{2y^2(z+x)}} + \frac{z^2+xy}{\sqrt{2z^2(x+y)}} \geq1\]
by Ashfaq Uday
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.
by Ashfaq Uday
Tue Nov 08, 2011 9:14 pm
Forum: Algebra
Topic: Quadratic function
Replies: 0
Views: 912

Quadratic function

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??
by Ashfaq Uday
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.
by Ashfaq Uday
Mon Nov 07, 2011 9:17 pm
Forum: National Math Olympiad (BdMO)
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. :D
by Ashfaq Uday
Mon Nov 07, 2011 9:07 pm
Forum: National Math Olympiad (BdMO)
Topic: Problems Involving Triangles
Replies: 8
Views: 2725

Re: Problems Involving Triangles

Number 2. \[13/2,5\]
@tiham, rookie mistake :?
by Ashfaq Uday
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??
by Ashfaq Uday
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. :D
by Ashfaq Uday
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??