Question

the $\max$ of $\min$

score 77 · Answer 1 · 2026-04-30 02:45:23

77

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the $\max$ of $\min$

Published on 30 Apr 2026 - 2:45

score 105 · Answer 2 · 2026-03-25 09:43:11

105

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Inequality $\sum_{cyc}\frac{a^{60}}{\frac{11}{2}a^{50}+5b^{50}}\geq 2\frac{a^{10}+b^{10}+c^{10}}{21}$

Published on 25 Mar 2026 - 9:43

score 383 · Answer 3 · 2026-04-06 07:42:37

383

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Prove or Disprove this statement .

Published on 06 Apr 2026 - 7:42

score 84 · Answer 4 · 2026-03-25 09:43:08

84

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Inequality $\sqrt{\frac{(ab)^2+(bc)^2+(ca)^2}{a^4+b^4+c^4}}\Big(\sum_{cyc}\frac{a^2}{7a+5b}\Big)+\frac{(a-b)^2}{12}\leq \frac{1}{12}$

Published on 25 Mar 2026 - 9:43

score 84 · Answer 5 · 2026-03-25 09:43:07

Inequality $\Big(\frac{a}{a^{10}+1}+\frac{b}{b^{10}+1}+\frac{c}{c^{10}+1}\Big)\Big(\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}\Big)\leq \frac{9}{4}$

score 40 · Answer 6 · 2026-04-06 07:42:25

40

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Prove or disprove this statement

Published on 06 Apr 2026 - 7:42

score 213 · Answer 7 · 2026-04-16 16:51:35

213

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Inequality involving the angle bisectors of a triangle

Published on 16 Apr 2026 - 16:51

score 77 · Answer 8 · 2026-03-25 09:40:50

77

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How find the maximum of the value $t$ such $x^3+y^3+z^3+t(xy^2+yz^2+zx^2)\ge (1+t)(x^2y+y^2z+z^2x)$

Published on 25 Mar 2026 - 9:40

score 192 · Answer 9 · 2026-03-25 09:39:45

192

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For positive a,b,c,d, if $a^2+b^2+c^2+d^2+abcd=5$, show $a+b+c+d\leq 4$.

Published on 25 Mar 2026 - 9:39

score 64 · Answer 10 · 2026-03-25 09:39:44

64

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How prove this inequality $9c^2(a+c)(a+2b+c)\le 2(a+b+c)(ab+bc+ac)(4c+a+b)$

Published on 25 Mar 2026 - 9:39

score 139 · Answer 11 · 2026-03-25 09:40:00

139

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Prove $\Big[\sum\limits_{cyc} a(a^2+2bc)\Big]^3 \geqq 3(ab+bc+ca)^2 . \sum\limits_{cyc} a(a^2+2bc)^2$

Published on 25 Mar 2026 - 9:40

score 147 · Answer 12 · 2026-03-25 09:43:13

147

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Prove $\frac{a^2}{(b+c)^2}+\frac{b^2}{(c+a)^2}+\frac{c^2}{(a+b)^2}+\frac{1}{4}\ge \frac{a^2+b^2+c^2}{ab+bc+ca}$

Published on 25 Mar 2026 - 9:43

score 182 · Answer 13 · 2026-03-25 09:39:54

182

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Alternative proofs of $a^2+b^2+c^2 \geqslant \frac{9abc}{a+b+c}+2(1+\sqrt 2)(a-b)(b-c)$

Published on 25 Mar 2026 - 9:39

score 226 · Answer 14 · 2026-03-25 09:39:54

226

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Prove $\frac{a(b+c)}{b^2+bc+c^2} \geqslant \frac{8a^2+2a(b+c)-(b-c)^2}{3(a^2+b^2+c^2+ab+bc+ca)}.$

Published on 25 Mar 2026 - 9:39

score 112 · Answer 15 · 2026-04-06 07:43:38

112

Views

Prove this inequality with $xyz=1$

Published on 06 Apr 2026 - 7:43

List Question

the $\max$ of $\min$

Inequality $\sum_{cyc}\frac{a^{60}}{\frac{11}{2}a^{50}+5b^{50}}\geq 2\frac{a^{10}+b^{10}+c^{10}}{21}$

Prove or Disprove this statement .

Inequality $\sqrt{\frac{(ab)^2+(bc)^2+(ca)^2}{a^4+b^4+c^4}}\Big(\sum_{cyc}\frac{a^2}{7a+5b}\Big)+\frac{(a-b)^2}{12}\leq \frac{1}{12}$

Inequality $\Big(\frac{a}{a^{10}+1}+\frac{b}{b^{10}+1}+\frac{c}{c^{10}+1}\Big)\Big(\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}\Big)\leq \frac{9}{4}$

Prove or disprove this statement

Inequality involving the angle bisectors of a triangle

How find the maximum of the value $t$ such $x^3+y^3+z^3+t(xy^2+yz^2+zx^2)\ge (1+t)(x^2y+y^2z+z^2x)$

For positive a,b,c,d, if $a^2+b^2+c^2+d^2+abcd=5$, show $a+b+c+d\leq 4$.

How prove this inequality $9c^2(a+c)(a+2b+c)\le 2(a+b+c)(ab+bc+ac)(4c+a+b)$

Prove $\Big[\sum\limits_{cyc} a(a^2+2bc)\Big]^3 \geqq 3(ab+bc+ca)^2 . \sum\limits_{cyc} a(a^2+2bc)^2$

Prove $\frac{a^2}{(b+c)^2}+\frac{b^2}{(c+a)^2}+\frac{c^2}{(a+b)^2}+\frac{1}{4}\ge \frac{a^2+b^2+c^2}{ab+bc+ca}$

Alternative proofs of $a^2+b^2+c^2 \geqslant \frac{9abc}{a+b+c}+2(1+\sqrt 2)(a-b)(b-c)$

Prove $\frac{a(b+c)}{b^2+bc+c^2} \geqslant \frac{8a^2+2a(b+c)-(b-c)^2}{3(a^2+b^2+c^2+ab+bc+ca)}.$

Prove this inequality with $xyz=1$

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