inequality

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0 replies

jlacosta

Yesterday at 3:18 PM

0 replies

Number of solutions

Ecrin_eren 3

N 3 minutes ago by rchokler

The given equation is:

x³ + 4y³ + 2y = (2024 + 2y)(xy + 1)

The question asks for the number of integer solutions.

3 replies

Ecrin_eren

Today at 11:27 AM

rchokler

3 minutes ago

Geo Mock #8

Bluesoul 1

N an hour ago by vanstraelen

Consider acute triangle $ABC$ . Denote $M$ as the midpoint of $AB$ , and let $O$ be a point on segment $CM$ such that $\angle{AOB}=120^{\circ}$ . Find the length of $CM$ given $AO=5, BO=8, \angle{BAC}=60^{\circ}$ .

1 reply

Bluesoul

Apr 1, 2025

vanstraelen

an hour ago

Excalibur Identity

jjsunpu 3

N 3 hours ago by SomeonecoolLovesMaths

Hi I don't know if this counts or if this already exists but I proved that

using a pattern that I read about

0^2 = 0

1 - 0 = 1

1^2 = 1

4-1 = 3

2^2 = 4

9 - 4 = 5

3^2 = 9

the difference is the arithmetic sequence 2n+1

using this I got

k^2 =

3 replies

jjsunpu

5 hours ago

SomeonecoolLovesMaths

3 hours ago

An inequality

jokehim 6

N 3 hours ago by imnotgoodatmathsorry

Let $a,b,c \in \mathbb{R}: a+b+c=3$ then prove $\color{black}{\frac{a^2}{a^{2}-2a+3}+\frac{b^2}{b^{2}-2b+3}+\frac{c^2}{c^{2}-2c+3}\ge \frac{3}{2}.}$

6 replies

jokehim

Mar 21, 2025

imnotgoodatmathsorry

3 hours ago

No more topics!

inequality

sunshine_12 2

N Mar 30, 2025 by sunshine_12

|a| + |b| + |c| − |a + b| − |b + c| − |c + a| + |a + b + c| ≥ 0
hey everyone, so I came across this inequality, and I did make some progress:
Let (a+b), (b+c), (c+a) be three sums T1, T2 and T3. As there are 3 sums, but they can be of only 2 signs, by pigeon hole principle, atleast 2 of the 3 sums must be of the same sign.
But I'm getting stuck on the case work. Can anyone help?
Thnx a lot

2 replies