Question

Proving $abcd+3\geq a+b+c+d$

score 1k · Answer 1 · 2021-01-18 14:00:38

1k

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Proving $abcd+3\geq a+b+c+d$

Published on 18 Jan 2021 - 14:00

score 153 · Answer 2 · 2021-02-06 05:14:23

153

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If$x^2+y^2+z^2+t^2=x(y+z+t)$prove $x=y=z=t=0$

Published on 06 Feb 2021 - 5:14

score 557 · Answer 3 · 2021-02-07 06:14:24

557

Views

Express $169$ as the sum of $1,2,3,4,5$ non-zero squares

Published on 07 Feb 2021 - 6:14

score 134 · Answer 4 · 2021-02-10 03:21:48

134

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Simplifying this equation to get sum of squares

Published on 10 Feb 2021 - 3:21

score 119 · Answer 5 · 2021-02-23 07:12:11

119

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SOSTOOLS - Express a Matrix polynomials as Polynomial

Published on 23 Feb 2021 - 7:12

score 241 · Answer 6 · 2021-02-23 17:03:31

241

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Rational rank one decomposition of symmetric positive semidefinite integer matrices

Published on 23 Feb 2021 - 17:03

score 178 · Answer 7 · 2026-03-26 07:35:32

178

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To need a way of thinking about Ji_Chen's nice result $(a- c)^{2}+ (b- d)^{2}\geq\frac{7}{9}ab- \frac{7}{20}(c^{2}+ 4d^{2})$

Published on 26 Mar 2026 - 7:35

score 109 · Answer 8 · 2021-02-27 01:36:31

109

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Question about Sui Zhen Lin's proof for inequality $\sqrt{\frac{a^2}{9b^2-8b+4}}+\sqrt{\frac{4b}{a+4}}\leq 1$ with positive numbers $a,b$ so $a+b=1$

Published on 27 Feb 2021 - 1:36

score 93 · Answer 9 · 2021-02-27 07:54:17

93

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Trigonometric Equation - can this be solved using complex numbers

Published on 27 Feb 2021 - 7:54

score 433 · Answer 10 · 2026-03-25 03:04:12

433

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Prove that there exist four polynomials $p_1,p_2,p_3,p_4$ in $x,y,z$ so that $(x^2+y^2+z^2)^3-8(z^3x^3+x^3y^3+y^3z^3)=p_1^2+p_2^2+p_3^2+p_4^2$

Published on 25 Mar 2026 - 3:04

score 573 · Answer 11 · 2026-03-26 12:38:25

573

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Find $g(x,y,z);p(x,y,z)\ge 0$ so that $f(x,y,z):=x\cdot g(x,y,z)+p(x,y,z)$

Published on 26 Mar 2026 - 12:38

score 267 · Answer 12 · 2026-03-25 17:40:46

267

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Choi Lam homogeneous polynomials as sums of squares

Published on 25 Mar 2026 - 17:40

score 212 · Answer 13 · 2026-03-25 17:42:18

212

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Can any polynomial in $\Bbb R [x]$ be written as the difference of two sum-of-squares polynomials in $\Bbb R [x]$?

Published on 25 Mar 2026 - 17:42

score 104 · Answer 14 · 2021-03-27 16:10:17

104

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solving $\sqrt{2 x^4-3 x^2+1}+\sqrt{2x^4-x^2}=4 x-3.$

Published on 27 Mar 2021 - 16:10

score 117 · Answer 15 · 2026-03-26 01:03:27

117

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Prove that $a^3b^3 + b^3 + 1 \geq a^2b^2 + ab^3 + b$ (for real, positive $a$,$b$

Published on 26 Mar 2026 - 1:03

List Question

Proving $abcd+3\geq a+b+c+d$

If$x^2+y^2+z^2+t^2=x(y+z+t)$prove $x=y=z=t=0$

Express $169$ as the sum of $1,2,3,4,5$ non-zero squares

Simplifying this equation to get sum of squares

SOSTOOLS - Express a Matrix polynomials as Polynomial

Rational rank one decomposition of symmetric positive semidefinite integer matrices

To need a way of thinking about Ji_Chen's nice result $(a- c)^{2}+ (b- d)^{2}\geq\frac{7}{9}ab- \frac{7}{20}(c^{2}+ 4d^{2})$

Question about Sui Zhen Lin's proof for inequality $\sqrt{\frac{a^2}{9b^2-8b+4}}+\sqrt{\frac{4b}{a+4}}\leq 1$ with positive numbers $a,b$ so $a+b=1$

Trigonometric Equation - can this be solved using complex numbers

Prove that there exist four polynomials $p_1,p_2,p_3,p_4$ in $x,y,z$ so that $(x^2+y^2+z^2)^3-8(z^3x^3+x^3y^3+y^3z^3)=p_1^2+p_2^2+p_3^2+p_4^2$

Find $g(x,y,z);p(x,y,z)\ge 0$ so that $f(x,y,z):=x\cdot g(x,y,z)+p(x,y,z)$

Choi Lam homogeneous polynomials as sums of squares

Can any polynomial in $\Bbb R [x]$ be written as the difference of two sum-of-squares polynomials in $\Bbb R [x]$?

solving $\sqrt{2 x^4-3 x^2+1}+\sqrt{2x^4-x^2}=4 x-3.$

Prove that $a^3b^3 + b^3 + 1 \geq a^2b^2 + ab^3 + b$ (for real, positive $a$,$b$

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