Question

Prove that if $a,b,c$ are sides of a triangle and $s$ is the semi-perimeter, then $a^2+b^2+c^2 \geq \dfrac{36}{35}\bigg(s^2 + \dfrac{abc}{s}\bigg)$

score 309 · Answer 1 · 2026-04-15 21:08:16

309

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Prove that if $a,b,c$ are sides of a triangle and $s$ is the semi-perimeter, then $a^2+b^2+c^2 \geq \dfrac{36}{35}\bigg(s^2 + \dfrac{abc}{s}\bigg)$

Published on 15 Apr 2026 - 21:08

score 124 · Answer 2 · 2026-04-23 10:23:33

124

Views

Solving $\dfrac{x}{1-e^{-x}} = 3.034$

Published on 23 Apr 2026 - 10:23

score 118 · Answer 3 · 2026-04-14 22:50:06

118

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Is it possible to solve for $t$ in $\frac{at(1+t)^d}{(1+t)^d-1} = m $?

Published on 14 Apr 2026 - 22:50

score 126 · Answer 4 · 2026-04-17 00:47:39

126

Views

Given $a,b,c$ are sides of a triangle, Prove that :- $\frac{1}{3} \leq \frac{a^2+b^2+c^2}{(a+b+c)^2} < \frac{1}{2}$

Published on 17 Apr 2026 - 0:47

score 38 · Answer 5 · 2026-04-13 22:08:34

Possible error in the solution write up for the problem of evaluating $\int_{0}^{1} (-1)^{[nt]}(-1)^{[mt]}dt$ if $m$ and $n$ are positive integers

score 151 · Answer 6 · 2026-04-13 04:28:53

151

Views

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score 115 · Answer 7 · 2026-04-13 09:18:06

115

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63

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score 120 · Answer 9 · 2026-04-14 00:20:32

120

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Problem 102 from Pólya-Szegő book

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score 205 · Answer 10 · 2026-04-13 09:56:01

205

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score 53 · Answer 11 · 2026-04-16 00:48:25

53

Views

$\frac{dx}{dt} = x-xy,\quad \frac{dy}{dt} = -y+xy.$ Find the range of values of $\ x\ $ and $\ y\ $ for which both variables are increasing.

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152

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score 89 · Answer 14 · 2026-04-16 17:42:04

89

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score 1.6k · Answer 15 · 2026-03-30 22:41:07

1.6k

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Differential equation: mixing salt into water problem where there is also leakage. Is my differential equation correct, and how to solve?

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List Question

Prove that if $a,b,c$ are sides of a triangle and $s$ is the semi-perimeter, then $a^2+b^2+c^2 \geq \dfrac{36}{35}\bigg(s^2 + \dfrac{abc}{s}\bigg)$

Solving $\dfrac{x}{1-e^{-x}} = 3.034$

Is it possible to solve for $t$ in $\frac{at(1+t)^d}{(1+t)^d-1} = m $?

Given $a,b,c$ are sides of a triangle, Prove that :- $\frac{1}{3} \leq \frac{a^2+b^2+c^2}{(a+b+c)^2} < \frac{1}{2}$

Possible error in the solution write up for the problem of evaluating $\int_{0}^{1} (-1)^{[nt]}(-1)^{[mt]}dt$ if $m$ and $n$ are positive integers

Conflict of methods :- "How many 3 digit natural numbers less than 1000 and divisible by 5 are there such that all digits are distinct "?

How to decompose $\frac{1+x}{\sqrt{(1-x)}}$ into partial fractions?

How to solve this work and time problem?

Problem 102 from Pólya-Szegő book

Questions related to problems from Polya-Szego's book

$\frac{dx}{dt} = x-xy,\quad \frac{dy}{dt} = -y+xy.$ Find the range of values of $\ x\ $ and $\ y\ $ for which both variables are increasing.

Probability of Rain Question

Problem 5.25 b baby rudin

Help solving equation $x^{ax}=(1-a+x)^{1-a+x}$

Differential equation: mixing salt into water problem where there is also leakage. Is my differential equation correct, and how to solve?

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