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15
Math.TechQA.Club
2019-05-30 07:40:38
2.3k
Views
IMO 1984: Prove that $0 ≤ yz + zx +xy −2xyz ≤ \frac {7}{27}$, where $x,y$ and $z$ are non-negative real numbers for which $x + y + z = 1.$
Published on
30 May 2019 - 7:40
#algebra-precalculus
#proof-verification
#inequality
#proof-writing
#contest-math
145
Views
Among any $5$ vertices there is a vertex connected to $4$ others. What is the minimum number of edges in such a graph with 40 vertices?
Published on
30 May 2019 - 8:15
#combinatorics
#graph-theory
#contest-math
120
Views
Is this a valid solution to Putnam 2017 A3?
Published on
30 May 2019 - 14:27
#calculus
#proof-verification
#contest-math
77
Views
Solve $x+y+z=3$; $x^3+y^3+z^3=15$; $x^5+y^5+z^5=83$
Published on
26 Mar 2026 - 3:01
#systems-of-equations
#contest-math
#symmetric-polynomials
118
Views
Olympiad inequality $\Big(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\Big)\sqrt{\frac{\prod_{cyc}(49x-7y+z)}{43^3}}\leq \sqrt{3(x+y+z)}$
Published on
31 May 2019 - 12:29
#inequality
#contest-math
151
Views
An olympiad question
Published on
31 May 2019 - 16:28
#contest-math
241
Views
30 languages spoken, how many participants are at the conference?
Published on
02 Jun 2019 - 16:37
#combinatorics
#discrete-mathematics
#contest-math
204
Views
Rationalizing $\frac{1}{\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}}$
Published on
26 Mar 2026 - 2:55
#algebra-precalculus
#contest-math
#symmetric-polynomials
457
Views
Advanced algebra-precalculus
Published on
04 Jun 2019 - 4:15
#algebra-precalculus
#contest-math
#real-numbers
65
Views
SMO 2012 Question 7
Published on
04 Jun 2019 - 18:49
#contest-math
464
Views
For $a,b,c,d > 0$ and $abcd = 1$, show that $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} + \frac{12}{a + b + c + d} \geq 7$
Published on
29 Mar 2026 - 0:50
#inequality
#contest-math
#alternative-proof
#uvw
#mixing-variables
104
Views
Prove that $n$ is Divisible by $6$ when the Quadratics have integer roots
Published on
28 Mar 2026 - 15:55
#number-theory
#contest-math
#divisibility
#quadratics
64
Views
Getting into competition math for an eager to learn high school student
Published on
06 Jun 2019 - 22:52
#contest-math
118
Views
Nice refinement of an inequality by Michael Rozenberg
Published on
25 Mar 2026 - 6:10
#inequality
#contest-math
#examples-counterexamples
#muirhead-inequality
50
Views
Suppose that * is an associative operation on a set S.
Published on
07 Jun 2019 - 16:59
#contest-math
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