Question

Find the maximum value of $2x^2 - 3xy - 2y^2$ subject to the condition that $25x^2 - 20xy + 40y^2 = 36$

score 1.3k · Answer 1 · 2018-06-12 13:24:03

1.3k

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Find the maximum value of $2x^2 - 3xy - 2y^2$ subject to the condition that $25x^2 - 20xy + 40y^2 = 36$

Published on 12 Jun 2018 - 13:24

score 1.8k · Answer 2 · 2026-03-26 08:00:39

1.8k

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a polynomial of degree $4$ such that $P(n) = \frac{120}{n}$ for $n=1,2,3,4,5$

Published on 26 Mar 2026 - 8:00

score 117 · Answer 3 · 2026-03-25 12:17:53

117

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find $f(99)$ where $2f(x-\frac{1}{x}) + f(\frac{1}{x}-x) = 3(x+\frac{1}{x})^2.$

Published on 25 Mar 2026 - 12:17

score 289 · Answer 4 · 2018-06-13 09:48:51

289

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Online Math Olympiad courses

Published on 13 Jun 2018 - 9:48

score 111 · Answer 5 · 2018-06-13 19:05:50

111

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2000 AIME II Problem: Trapped by a Trapezoid

Published on 13 Jun 2018 - 19:05

score 214 · Answer 6 · 2018-06-14 23:37:46

214

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How did Wikipedia derive this inequality for increasing functions: $\int_{a-1}^{b} f(s)\ ds \le \sum_{i=a}^{b} f(i) \le \int_{a}^{b+1} f(s)\ ds$

Published on 14 Jun 2018 - 23:37

score 144 · Answer 7 · 2026-03-26 04:51:37

144

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find the maximum possible value of $n_9-n_1$

Published on 26 Mar 2026 - 4:51

score 108 · Answer 8 · 2026-03-25 22:23:52

108

Views

overline over numbers and other stuff

Published on 25 Mar 2026 - 22:23

score 246 · Answer 9 · 2026-03-26 11:01:25

246

Views

Find the value of $\frac{4x}{y+1} + \frac{16y}{z+1} + \frac{64z}{x+1}$

Published on 26 Mar 2026 - 11:01

score 94 · Answer 10 · 2018-06-16 21:50:57

94

Views

Find a segment length in geometric problem (figure provided).

Published on 16 Jun 2018 - 21:50

score 219 · Answer 11 · 2018-06-16 22:31:22

219

Views

Induction Problem from Putnam and Beyond

Published on 16 Jun 2018 - 22:31

score 160 · Answer 12 · 2026-03-23 04:46:23

160

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If $0⩽x⩽y⩽z⩽w⩽u$ and $x+y+z+w+u=1$, prove $xw+wz+zy+yu+ux⩽\frac15$

Published on 23 Mar 2026 - 4:46

score 1.1k · Answer 13 · 2026-03-26 07:57:01

1.1k

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prove that the three points are collinear

Published on 26 Mar 2026 - 7:57

score 164 · Answer 14 · 2026-03-25 14:24:36

164

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Proving $abc(x+y+z)^2\geq a(1-2a)yz+b(1-2b)xz+c(1-2c)xy.$

Published on 25 Mar 2026 - 14:24

score 75 · Answer 15 · 2026-03-25 12:45:33

75

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finding $a_{2016}$

Published on 25 Mar 2026 - 12:45

List Question

Find the maximum value of $2x^2 - 3xy - 2y^2$ subject to the condition that $25x^2 - 20xy + 40y^2 = 36$

a polynomial of degree $4$ such that $P(n) = \frac{120}{n}$ for $n=1,2,3,4,5$

find $f(99)$ where $2f(x-\frac{1}{x}) + f(\frac{1}{x}-x) = 3(x+\frac{1}{x})^2.$

Online Math Olympiad courses

2000 AIME II Problem: Trapped by a Trapezoid

How did Wikipedia derive this inequality for increasing functions: $\int_{a-1}^{b} f(s)\ ds \le \sum_{i=a}^{b} f(i) \le \int_{a}^{b+1} f(s)\ ds$

find the maximum possible value of $n_9-n_1$

overline over numbers and other stuff

Find the value of $\frac{4x}{y+1} + \frac{16y}{z+1} + \frac{64z}{x+1}$

Find a segment length in geometric problem (figure provided).

Induction Problem from Putnam and Beyond

If $0⩽x⩽y⩽z⩽w⩽u$ and $x+y+z+w+u=1$, prove $xw+wz+zy+yu+ux⩽\frac15$

prove that the three points are collinear

Proving $abc(x+y+z)^2\geq a(1-2a)yz+b(1-2b)xz+c(1-2c)xy.$

finding $a_{2016}$

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