User user2838619

1

13

votes

2

answers

432

views

Solving $x_1+x_2=x_3^2, x_2+x_3=x_4^2, x_3+x_4=x_5^2,x_4+x_5=x_1^2, x_5+x_1=x_2^2$ in reals

algebra-precalculus systems-of-equations

Apr 5 '17 at 12:50 walak 251

3

9

votes

7

answers

2k

views

How many $10$ digit number exists that sum of their digits is equal to $15$?

combinatorics combinations

Jul 30 '14 at 0:32 miracle173 8,685

2

8

votes

2

answers

341

views

Prove two of $\frac{2}{a}+\frac{3}{b}+\frac{6}{c}\geq 6,\frac{2}{b}+\frac{3}{c}+\frac{6}{a}\geq 6,\frac{2}{c}+\frac{3}{a}+\frac{6}{b}\geq 6$ are True

inequality

Dec 21 '15 at 13:07 Community♦ 1

5

8

votes

2

answers

338

views

prove $\frac {ab}{a+b} \geq \sum ^n_{i=1} \frac{a_ib_i}{a_i+b_i}$

inequality

Jul 30 '14 at 11:04 Jonas Dahlbæk 4,063

4

7

votes

2

answers

351

views

Solve $x+3y=4y^3,y+3z=4z^3 ,z+3x=4x^3$ in reals

algebra-precalculus polynomials systems-of-equations

Apr 21 at 12:14 Slade 27.6k

1

7

votes

6

answers

460

views

Prove that $\sum \limits_{cyc}\frac {a}{(b+c)^2} \geq \frac {9}{4(a+b+c)}$

inequality substitution symmetric-polynomials jensen-inequality tangent-line-method

May 18 '18 at 19:37 Gordon 4,131

3

7

votes

4

answers

1k

views

if $x+y+z=2$ and $xy+yz+zx=1$,Prove $x,y,z \in \left [0,\frac{4}{3} \right ]$

algebra-precalculus

Sep 8 '14 at 9:38 ShakesBeer 3,411

1

6

votes

3

answers

208

views

prove $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a} \geq 3(a^2+b^2+c^2)$

inequality

Jun 7 at 9:04 BestChoice123 316

4

6

votes

1

answer

286

views

Prove $a+b+c \geq ab+bc+ca$, given an additional constraint

inequality cauchy-schwarz-inequality a.m.-g.m.-inequality

May 26 at 13:15 Hanno 4,263

4

6

votes

3

answers

2k

views

Alternate proof for $a^2+b^2+c^2\le 9R^2$

geometry inequality triangles alternative-proof geometric-inequalities

Apr 15 '17 at 10:04 Michael Rozenberg 177k

1

6

votes

1

answer

1k

views

Prove of Nesbitt's inequality in 6 variables

inequality

Sep 15 '14 at 6:03 r9m 16.9k

6

votes

5

answers

130

views

Prove $a^2+b^2+c^2=\frac{6}{5}$ if $a+b+c=0$ and $a^3+b^3+c^3=a^5+b^5+c^5$

algebra-precalculus polynomials factoring

Sep 3 '14 at 6:45 Community♦ 1

1

5

votes

1

answer

374

views

Different solution for MOSP(Mathematical Olympiad Summer Program) 2001 Test 9 Problem

geometry contest-math

Nov 22 '14 at 21:11 Community♦ 1

1

5

votes

1

answer

171

views

Prove $\sin^{2m}\alpha\cdot\cos^{2n}\alpha\leq\frac{m^m n^n}{(m+n)^{(m+n)}}$

trigonometry inequality

Aug 15 '14 at 16:36 Michael Hardy 248k

1

5

votes

1

answer

123

views

Prove $\frac{(xy)^7}{x^8+(xy)^7+y^8}+\frac{(yz)^7}{y^8+(yz)^7+z^8}+\frac{(zx)^7}{z^8+(zx)^7+x^8}\leq1$

inequality

Aug 13 '14 at 7:18 Community♦ 1

5

votes

3

answers

197

views

Proving an inequality about a sequnce with Cauchy-Schwarz

inequality

Jul 30 '14 at 14:25 user2838619 2,818

4

votes

0

answers

610

views

net of oblique cone,why it has a shape like this?

geometry 3d rotations

Apr 8 at 23:12 Humberto José Bortolossi 172

1

4

votes

5

answers

303

views

Prove $\frac{a^3}{b^2}+\frac{b^3}{c^2}+\frac{c^3}{a^2} \geq \frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}$

inequality sum-of-squares-method

Jan 29 '20 at 12:52 tthnew 2,147

1

4

votes

3

answers

178

views

prove $\sum\limits_{cyc} \frac {a^3} {b+c+d} \geq \frac {1} {3}$

inequality polynomials factoring

Apr 11 '17 at 6:39 Michael Rozenberg 177k

2

4

votes

2

answers

179

views

Prove $\frac{ab}{1+c^2}+\frac{bc}{1+a^2}+\frac{ca}{1+b^2}\le\frac{3}{4}$ if $a^2+b^2+c^2=1$

inequality

Jan 18 '17 at 15:24 Community♦ 1

1

4

votes

3

answers

98

views

Prove $\frac{a}{(b-c)^2}+\frac{b}{(c-a)^2}+\frac{c}{(a-b)^2}=0$ if $\frac{a}{b-c}+\frac{b}{c-a}+\frac{c}{a-b}=0$

algebra-precalculus polynomials factoring

Sep 6 '14 at 6:18 Kelenner 18.2k

4

votes

2

answers

133

views

if $a$ is are real number that $a \neq 0$, and $\cos x = \sqrt{\frac{\cot x}{\cot x -a^2}}$, $x$ is on which trigonometric quadrants?

trigonometry

Aug 21 '14 at 20:47 Nick 6,280

2

4

votes

1

answer

206

views

Prove $\sum \limits_{cyc} \frac{1+b^2+c^4}{a^+b^2+c^3}\geq 3$

inequality

Aug 1 '14 at 9:37 Macavity 40.1k

1

3

votes

2

answers

478

views

Prove $\frac{ab}{\sqrt{2c+a+b}}+\frac{bc}{\sqrt{2a+b+c}}+\frac{ca}{\sqrt{2b+c+a}}\le\sqrt\frac{2}{3}$ if $a+b+c=2$

inequality summation a.m.-g.m.-inequality cauchy-schwarz-inequality

Dec 8 '19 at 5:18 Michael Rozenberg 177k

2

3

votes

2

answers

272

views

prove $\sum \limits_{cyc} \frac{x}{x+\sqrt{(x+y)(x+z)}}\leq 1$

inequality

Nov 21 '18 at 3:07 Michael Rozenberg 177k

1

3

votes

0

answers

311

views

Longest simple path and minimum degree

graph-theory

May 2 '18 at 7:52 Community♦ 1

3

votes

3

answers

129

views

Proving Cauchy inequality involving four expression

inequality cauchy-schwarz-inequality muirhead-inequality

Aug 27 '17 at 10:03 Michael Rozenberg 177k

3

votes

1

answer

334

views

proving irrationality of cube-root of 2 using an specific method?

alternative-proof irrational-numbers

Feb 2 '17 at 9:30 Especially Lime 33k

1

3

votes

2

answers

158

views

Prove $\sum\limits_{cyc} \frac{\sqrt{xy}}{\sqrt{xy+z}}\le\frac{3}{2}$ if $x+y+z=1$

inequality

Oct 20 '16 at 13:39 Michael Rozenberg 177k

1

3

votes

2

answers

1k

views

number of ways to put 4 black,4 white,4 red balls in 6 different boxes

combinatorics

Aug 11 '15 at 4:03 user3837690 19

Stack Exchange Network

current community

your communities

more stack exchange communities

Next privilege

Next badge

73 Questions

Solving $x_1+x_2=x_3^2, x_2+x_3=x_4^2, x_3+x_4=x_5^2,x_4+x_5=x_1^2, x_5+x_1=x_2^2$ in reals

How many $10$ digit number exists that sum of their digits is equal to $15$?

Prove two of $\frac{2}{a}+\frac{3}{b}+\frac{6}{c}\geq 6,\frac{2}{b}+\frac{3}{c}+\frac{6}{a}\geq 6,\frac{2}{c}+\frac{3}{a}+\frac{6}{b}\geq 6$ are True

prove $\frac {ab}{a+b} \geq \sum ^n_{i=1} \frac{a_ib_i}{a_i+b_i}$

Solve $x+3y=4y^3,y+3z=4z^3 ,z+3x=4x^3$ in reals

Prove that $\sum \limits_{cyc}\frac {a}{(b+c)^2} \geq \frac {9}{4(a+b+c)}$

if $x+y+z=2$ and $xy+yz+zx=1$,Prove $x,y,z \in \left [0,\frac{4}{3} \right ]$

prove $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a} \geq 3(a^2+b^2+c^2)$

Prove $a+b+c \geq ab+bc+ca$, given an additional constraint

Alternate proof for $a^2+b^2+c^2\le 9R^2$

Prove of Nesbitt's inequality in 6 variables

Prove $a^2+b^2+c^2=\frac{6}{5}$ if $a+b+c=0$ and $a^3+b^3+c^3=a^5+b^5+c^5$

Different solution for MOSP(Mathematical Olympiad Summer Program) 2001 Test 9 Problem

Prove $\sin^{2m}\alpha\cdot\cos^{2n}\alpha\leq\frac{m^m n^n}{(m+n)^{(m+n)}}$

Prove $\frac{(xy)^7}{x^8+(xy)^7+y^8}+\frac{(yz)^7}{y^8+(yz)^7+z^8}+\frac{(zx)^7}{z^8+(zx)^7+x^8}\leq1$

Proving an inequality about a sequnce with Cauchy-Schwarz

net of oblique cone,why it has a shape like this?

Prove $\frac{a^3}{b^2}+\frac{b^3}{c^2}+\frac{c^3}{a^2} \geq \frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}$

prove $\sum\limits_{cyc} \frac {a^3} {b+c+d} \geq \frac {1} {3}$

Prove $\frac{ab}{1+c^2}+\frac{bc}{1+a^2}+\frac{ca}{1+b^2}\le\frac{3}{4}$ if $a^2+b^2+c^2=1$

Prove $\frac{a}{(b-c)^2}+\frac{b}{(c-a)^2}+\frac{c}{(a-b)^2}=0$ if $\frac{a}{b-c}+\frac{b}{c-a}+\frac{c}{a-b}=0$

if $a$ is are real number that $a \neq 0$, and $\cos x = \sqrt{\frac{\cot x}{\cot x -a^2}}$, $x$ is on which trigonometric quadrants?

Prove $\sum \limits_{cyc} \frac{1+b^2+c^4}{a^+b^2+c^3}\geq 3$

Prove $\frac{ab}{\sqrt{2c+a+b}}+\frac{bc}{\sqrt{2a+b+c}}+\frac{ca}{\sqrt{2b+c+a}}\le\sqrt\frac{2}{3}$ if $a+b+c=2$

prove $\sum \limits_{cyc} \frac{x}{x+\sqrt{(x+y)(x+z)}}\leq 1$

Longest simple path and minimum degree

Proving Cauchy inequality involving four expression

proving irrationality of cube-root of 2 using an specific method?

Prove $\sum\limits_{cyc} \frac{\sqrt{xy}}{\sqrt{xy+z}}\le\frac{3}{2}$ if $x+y+z=1$

number of ways to put 4 black,4 white,4 red balls in 6 different boxes