Question

How to prove that $ a^2+b^2+c^2=1$ implies $ab+bc+ca \in [-\frac12,1]$?

score 211 · Answer 1 · 2018-08-30 09:15:06

211

Views

How to prove that $ a^2+b^2+c^2=1$ implies $ab+bc+ca \in [-\frac12,1]$?

Published on 30 Aug 2018 - 9:15

score 426 · Answer 2 · 2018-08-31 21:29:56

426

Views

USAMTS $4/2/17$ Duck Goose Goose Problem

Published on 31 Aug 2018 - 21:29

score 301 · Answer 3 · 2026-03-26 11:03:13

301

Views

Prove $\sum\limits_{i=1}^n\frac1{x_i}\sqrt{x_i-x_{i-1}}\le\sum\limits_{i=1}^{n^2}\frac1i-\frac12$ for integers $1=x_0\le x_1\le x_2\le\cdots\le x_n$

Published on 26 Mar 2026 - 11:03

score 86 · Answer 4 · 2018-09-02 08:40:23

86

Views

Given $aabb$ is a square number, and $a := b$, find $a$ and $b$.

Published on 02 Sep 2018 - 8:40

score 773 · Answer 5 · 2026-03-25 09:29:03

773

Views

Number of binary strings of length $n$, where every $1$, if any, is followed by at most $k$ $0$s

Published on 25 Mar 2026 - 9:29

score 121 · Answer 6 · 2026-03-26 03:08:20

121

Views

Maximizing $x^2 y + y^2 z + z^2 x − x^2 z − y^2 x − z^2 y$ for $x$, $y$, $z$ between $0$ and $1$ (inclusive)

Published on 26 Mar 2026 - 3:08

score 304 · Answer 7 · 2018-09-02 20:48:33

304

Views

Confusion on 1990 B1 Putnam question

Published on 02 Sep 2018 - 20:48

score 63 · Answer 8 · 2018-09-03 05:39:07

63

Views

Difficulty in understanding a number theory problem

Published on 03 Sep 2018 - 5:39

score 94 · Answer 9 · 2018-09-04 03:50:49

94

Views

MATHCOUNTS States Team Problem #9 2018 (Sum of Terms are Squares)

Published on 04 Sep 2018 - 3:50

score 44 · Answer 10 · 2026-03-27 07:13:48

44

Views

Prove sum of angles in problem involving bisectors in a given triangle

Published on 27 Mar 2026 - 7:13

score 99 · Answer 11 · 2026-03-27 04:58:05

99

Views

Two points of a square $K$ determine a diagonal of another square that is contained in $K$

Published on 27 Mar 2026 - 4:58

score 224 · Answer 12 · 2026-03-27 08:56:04

224

Views

Find perimeter of right $\triangle ABC$, given segments defined on sides by bisectors

Published on 27 Mar 2026 - 8:56

score 178 · Answer 13 · 2026-03-25 22:05:15

178

Views

Permutation of points $P_i\in X$ such that $\sum^n_{j=1}|P_{\sigma(j+1)}-P_{\sigma(j)}|^2\leq 8$

Published on 25 Mar 2026 - 22:05

score 48 · Answer 14 · 2018-09-06 22:44:30

48

Views

$S(n)$ the set of all real roots of $p_n(x)$ where $p_{n+1}(x)=p(p_n(x))$, show that $S(n)\subseteq S(2n)$

Published on 06 Sep 2018 - 22:44

score 3.9k · Answer 15 · 2018-09-07 16:54:17

3.9k

Views

Find the number of complex numbers $z$ such that $z^{2018} =\overline{z}.$

Published on 07 Sep 2018 - 16:54

List Question

How to prove that $ a^2+b^2+c^2=1$ implies $ab+bc+ca \in [-\frac12,1]$?

USAMTS $4/2/17$ Duck Goose Goose Problem

Prove $\sum\limits_{i=1}^n\frac1{x_i}\sqrt{x_i-x_{i-1}}\le\sum\limits_{i=1}^{n^2}\frac1i-\frac12$ for integers $1=x_0\le x_1\le x_2\le\cdots\le x_n$

Given $aabb$ is a square number, and $a := b$, find $a$ and $b$.

Number of binary strings of length $n$, where every $1$, if any, is followed by at most $k$ $0$s

Maximizing $x^2 y + y^2 z + z^2 x − x^2 z − y^2 x − z^2 y$ for $x$, $y$, $z$ between $0$ and $1$ (inclusive)

Confusion on 1990 B1 Putnam question

Difficulty in understanding a number theory problem

MATHCOUNTS States Team Problem #9 2018 (Sum of Terms are Squares)

Prove sum of angles in problem involving bisectors in a given triangle

Two points of a square $K$ determine a diagonal of another square that is contained in $K$

Find perimeter of right $\triangle ABC$, given segments defined on sides by bisectors

Permutation of points $P_i\in X$ such that $\sum^n_{j=1}|P_{\sigma(j+1)}-P_{\sigma(j)}|^2\leq 8$

$S(n)$ the set of all real roots of $p_n(x)$ where $p_{n+1}(x)=p(p_n(x))$, show that $S(n)\subseteq S(2n)$

Find the number of complex numbers $z$ such that $z^{2018} =\overline{z}.$

Trending Questions

Popular # Hahtags

Popular Questions