Search found 6 matches

Return to advanced search

Re: BDMO Forum Mafia #1

I'll play. But I wanna know, how the cards will be distributed?
by Atonu Roy Chowdhury
Mon Mar 27, 2017 6:39 pm
 
Forum: Social Lounge
Topic: BDMO Forum Mafia #1
Replies: 24
Views: 433

Re: BDMO Forum Mafia

খেলা হবে। ✌✌✌
by Atonu Roy Chowdhury
Sat Mar 25, 2017 8:20 pm
 
Forum: Social Lounge
Topic: BDMO Forum Mafia
Replies: 5
Views: 107

HKTST 2016

Let $a,b,c$ be positive real numbers satisfying $abc=1$. Determine the smallest possible value of

$$\frac{a^3+8}{a^3(b+c)}+\frac{b^3+8}{b^3(a+c)}+\frac{c^3+8}{c^3(b+a)}$$
by Atonu Roy Chowdhury
Thu Mar 23, 2017 11:49 pm
 
Forum: Algebra
Topic: HKTST 2016
Replies: 1
Views: 45

Re: $2009$ USA TST Inequality

Just substitute $x = 1/a$, $y = 1/b$ and $z = 1/c$.
The rest is so cool.
by Atonu Roy Chowdhury
Thu Mar 23, 2017 11:36 pm
 
Forum: Algebra
Topic: $2009$ USA TST Inequality
Replies: 1
Views: 38

Re: Equation

x^2+xy+y^2=(x+y+3)^3/27,find all(x,y) It is obvious that $x+y$ is divisible by $3$ . Put $x+y$ = $3k$ . So, the equation becomes, $$(3k)^2 - x(3k-x) = (k+1)^3 $$ => $$ x^2 - 3kx + 9k^2 = k^3 + 3k^2 + 3k +1 $$ => $$ x^2 - 3kx - k^3 + 6k^2 - 3k -1 = 0 $$ As we have to find the integer roots of this e...
by Atonu Roy Chowdhury
Mon Mar 20, 2017 10:30 pm
 
Forum: Number Theory
Topic: Equation
Replies: 1
Views: 47

APMO 2013 P5

Let $ABCD$ be a quadrilateral inscribed in a circle $\omega$, and let $P$ be a point on the extension of $AC$ such that $PB$ and $PD$ are tangent to $\omega$. The tangent at $C$ intersects $PD$ at $Q$ and the line $AD$ at $R$. Let $E$ be the second point of intersection between $AQ$ and $\omega$. Pr...
by Atonu Roy Chowdhury
Fri Aug 19, 2016 8:17 pm
 
Forum: Geometry
Topic: APMO 2013 P5
Replies: 3
Views: 271

Return to advanced search

cron