Question

Let $a,b,c$ be positive reals. Find the minimum value of $P=\frac{a^2}{(a+b)^2}+\frac{b^2}{(b+c)^2}+\frac{c}{4a}$.

score 141 · Answer 1 · 2018-03-04 18:06:34

141

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Let $a,b,c$ be positive reals. Find the minimum value of $P=\frac{a^2}{(a+b)^2}+\frac{b^2}{(b+c)^2}+\frac{c}{4a}$.

Published on 04 Mar 2018 - 18:06

score 56 · Answer 2 · 2018-03-08 15:46:17

56

Views

2016 ARML Individual Problem #8. Tricky Substitutions to find coefficients of a polynomial

Published on 08 Mar 2018 - 15:46

score 165 · Answer 3 · 2018-03-12 14:35:45

165

Views

How can I show that $\int_{0}^1\int_{0}^1 \frac{1}{1-xy}dxdy=\frac{\pi^2}{6}$ through substitution?

Published on 12 Mar 2018 - 14:35

score 177 · Answer 4 · 2018-03-13 16:24:24

177

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Multivariable integration by substitution Part $2$

Published on 13 Mar 2018 - 16:24

score 81 · Answer 5 · 2018-03-15 08:55:06

81

Views

What is wrong with this substitution?

Published on 15 Mar 2018 - 8:55

score 533 · Answer 6 · 2018-03-19 01:54:58

533

Views

Inequality $\frac{a}{\sqrt{bc}}\cdot\frac1{a+1}+\frac{b}{\sqrt{ca}}\cdot\frac1{b+1}+\frac{c}{\sqrt{ab}}\cdot\frac1{c+1}\leqslant\sqrt2.$

Published on 19 Mar 2018 - 1:54

score 9.1k · Answer 7 · 2026-03-21 20:43:38

9.1k

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Back substitution in Python

Published on 21 Mar 2026 - 20:43

score 168 · Answer 8 · 2018-03-21 18:53:48

168

Views

Change of Variables by u substitution

Published on 21 Mar 2018 - 18:53

score 70 · Answer 9 · 2018-03-22 08:23:21

70

Views

I don't understand this u-sub step..

Published on 22 Mar 2018 - 8:23

score 20k · Answer 10 · 2018-03-22 12:38:10

20k

Views

Solutions of recurrence relations $T(n) = 2T(n-1)$ and $T(n) = 2T(n-1) - 1$

Published on 22 Mar 2018 - 12:38

score 89 · Answer 11 · 2018-03-23 06:45:45

89

Views

Is $\frac{cos^4(x)}{4}-\frac{cos^2(x)}{2}+C$ a correct evalution of $\int sin^3(x)cos(x)\ dx$

Published on 23 Mar 2018 - 6:45

score 154 · Answer 12 · 2018-03-24 14:39:07

154

Views

How to solve $\int \frac{\mathrm dx}{3x^2-7}$?

Published on 24 Mar 2018 - 14:39

score 102 · Answer 13 · 2018-03-25 20:18:40

102

Views

Evaluate $\int \frac{1}{ax^2-bx}\,dx$ with substitution

Published on 25 Mar 2018 - 20:18

score 111 · Answer 14 · 2018-03-27 14:59:02

111

Views

Let $a> 0, b> 0$. Prove that: $\frac{{{a}^{2}}}{b}+\frac{{{b}^{2}}}{a}+7\left( a+b \right)\ge 8\sqrt{2\left( {{a}^{2}}+{{b}^{2}} \right)}$

Published on 27 Mar 2018 - 14:59

score 298 · Answer 15 · 2026-03-22 03:56:18

298

Views

Idempotent substitution $\theta$

Published on 22 Mar 2026 - 3:56

List Question

Let $a,b,c$ be positive reals. Find the minimum value of $P=\frac{a^2}{(a+b)^2}+\frac{b^2}{(b+c)^2}+\frac{c}{4a}$.

2016 ARML Individual Problem #8. Tricky Substitutions to find coefficients of a polynomial

How can I show that $\int_{0}^1\int_{0}^1 \frac{1}{1-xy}dxdy=\frac{\pi^2}{6}$ through substitution?

Multivariable integration by substitution Part $2$

What is wrong with this substitution?

Inequality $\frac{a}{\sqrt{bc}}\cdot\frac1{a+1}+\frac{b}{\sqrt{ca}}\cdot\frac1{b+1}+\frac{c}{\sqrt{ab}}\cdot\frac1{c+1}\leqslant\sqrt2.$

Back substitution in Python

Change of Variables by u substitution

I don't understand this u-sub step..

Solutions of recurrence relations $T(n) = 2T(n-1)$ and $T(n) = 2T(n-1) - 1$

Is $\frac{cos^4(x)}{4}-\frac{cos^2(x)}{2}+C$ a correct evalution of $\int sin^3(x)cos(x)\ dx$

How to solve $\int \frac{\mathrm dx}{3x^2-7}$?

Evaluate $\int \frac{1}{ax^2-bx}\,dx$ with substitution

Let $a> 0, b> 0$. Prove that: $\frac{{{a}^{2}}}{b}+\frac{{{b}^{2}}}{a}+7\left( a+b \right)\ge 8\sqrt{2\left( {{a}^{2}}+{{b}^{2}} \right)}$

Idempotent substitution $\theta$

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