Question

How to solve $\sqrt{\frac{a}{bc+2}}+\sqrt{\frac{b}{ca+2}}+\sqrt{\frac{c}{ab+2}}\le \sqrt{\frac{3}{2}}\cdot\sqrt{a+b+c-1}$?

score 95 · Answer 1 · 2026-03-26 08:00:26

95

Views

How to solve $\sqrt{\frac{a}{bc+2}}+\sqrt{\frac{b}{ca+2}}+\sqrt{\frac{c}{ab+2}}\le \sqrt{\frac{3}{2}}\cdot\sqrt{a+b+c-1}$?

Published on 26 Mar 2026 - 8:00

score 84 · Answer 2 · 2026-03-26 09:42:43

84

Views

Inequality sum of square root $3a^3+bc$ when $a^2+b^2+c^2=3$.

Published on 26 Mar 2026 - 9:42

score 132 · Answer 3 · 2026-03-25 16:20:36

132

Views

Find a nice proof for an elegant problem.

Published on 25 Mar 2026 - 16:20

score 47 · Answer 4 · 2023-12-04 20:13:44

47

Views

Proving by induction a result relating to elementary symmetric functions

Published on 04 Dec 2023 - 20:13

score 84 · Answer 5 · 2026-03-26 11:00:56

84

Views

Proving $\sqrt{31a+b+c} +\sqrt{31b+a+c} +\sqrt{31c+b+a}\le 3\sqrt{3}\cdot\sqrt{a+b+c+8}$? when $a+b+c+abc=4.$

Published on 26 Mar 2026 - 11:00

score 119 · Answer 6 · 2026-03-26 11:00:54

119

Views

Proving $\sum_{cyc}\frac{a}{\sqrt{8a+bc}}\le \frac{\sqrt{a+b+c+abc}}{2}$ if $ab+bc+ca=3.$

Published on 26 Mar 2026 - 11:00

score 126 · Answer 7 · 2026-03-26 09:39:59

126

Views

$a+b+c−3≥k(a−b)(b−c)(c−a)$

Published on 26 Mar 2026 - 9:39

score 150 · Answer 8 · 2026-03-26 12:53:57

150

Views

Proving $5(a^2+b^2+c^2)+ab+bc+ca\ge 2\sum_{cyc}a\sqrt{5a^2+b^2+c^2+ab+ac}.$

Published on 26 Mar 2026 - 12:53

score 41 · Answer 9 · 2023-12-11 10:22:51

41

Views

Proving the uniqueness of the representation of the fundamental theorem on symmetric polynomials.

Published on 11 Dec 2023 - 10:22

score 27 · Answer 10 · 2023-12-14 14:43:47

27

Views

Express polynomial in terms of elemetary symmetric functions

Published on 14 Dec 2023 - 14:43

score 103 · Answer 11 · 2024-01-01 16:41:16

103

Views

Coefficient of polynomial of $x^k$

Published on 01 Jan 2024 - 16:41

score 69 · Answer 12 · 2024-01-02 10:59:18

69

Views

Prove $\sigma_{n-1}\ge2n-n^2+(n-1)\sigma_1$ for $(x_1\dots,x_n)\in[0,1]^n$

Published on 02 Jan 2024 - 10:59

score 106 · Answer 13 · 2026-02-23 08:31:49

106

Views

Galois theory and Lagrange's method on quintics

Published on 23 Feb 2026 - 8:31

score 57 · Answer 14 · 2026-03-26 08:04:05

57

Views

Generating Function for Modified Multinomial Coefficients

Published on 26 Mar 2026 - 8:04

score 95 · Answer 15 · 2024-01-22 12:34:21

95

Views

What is the value of $a^2+b^2+c^2+d^2$ and $a^3+b^3+c^3+d^3$ for $a,b,c,d$ roots of $f(x)=(x-1)^2(x-2)^2+1$

Published on 22 Jan 2024 - 12:34

List Question

How to solve $\sqrt{\frac{a}{bc+2}}+\sqrt{\frac{b}{ca+2}}+\sqrt{\frac{c}{ab+2}}\le \sqrt{\frac{3}{2}}\cdot\sqrt{a+b+c-1}$?

Inequality sum of square root $3a^3+bc$ when $a^2+b^2+c^2=3$.

Find a nice proof for an elegant problem.

Proving by induction a result relating to elementary symmetric functions

Proving $\sqrt{31a+b+c} +\sqrt{31b+a+c} +\sqrt{31c+b+a}\le 3\sqrt{3}\cdot\sqrt{a+b+c+8}$? when $a+b+c+abc=4.$

Proving $\sum_{cyc}\frac{a}{\sqrt{8a+bc}}\le \frac{\sqrt{a+b+c+abc}}{2}$ if $ab+bc+ca=3.$

$a+b+c−3≥k(a−b)(b−c)(c−a)$

Proving $5(a^2+b^2+c^2)+ab+bc+ca\ge 2\sum_{cyc}a\sqrt{5a^2+b^2+c^2+ab+ac}.$

Proving the uniqueness of the representation of the fundamental theorem on symmetric polynomials.

Express polynomial in terms of elemetary symmetric functions

Coefficient of polynomial of $x^k$

Prove $\sigma_{n-1}\ge2n-n^2+(n-1)\sigma_1$ for $(x_1\dots,x_n)\in[0,1]^n$

Galois theory and Lagrange's method on quintics

Generating Function for Modified Multinomial Coefficients

What is the value of $a^2+b^2+c^2+d^2$ and $a^3+b^3+c^3+d^3$ for $a,b,c,d$ roots of $f(x)=(x-1)^2(x-2)^2+1$

Trending Questions

Popular # Hahtags

Popular Questions