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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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Proof Marathon
ReticulatedPython   4
N 2 hours ago by StrahdVonZarovich
You can post any interesting proof-based problems here that are high school level.

Rule(s): A proof must be provided to the most recent problem before a new one is posted.
4 replies
ReticulatedPython
5 hours ago
StrahdVonZarovich
2 hours ago
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Inequalities from SXTX
sqing   16
N 4 hours ago by DAVROS
T702. Let $ a,b,c>0 $ and $ a+2b+3c=\sqrt{13}. $ Prove that $$ \sqrt{a^2+1} +2\sqrt{b^2+1} +3\sqrt{c^2+1} \geq 7$$S
T703. Let $ a,b $ be real numbers such that $ a+b\neq 0. $. Find the minimum of $ a^2+b^2+(\frac{1-ab}{a+b} )^2.$
T704. Let $ a,b,c>0 $ and $ a+b+c=3. $ Prove that $$ \frac{a^2+7}{(c+a)(a+b)} + \frac{b^2+7}{(a+b)(b+c)} +\frac{c^2+7}{(b+c)(c+a)} \geq 6$$S
16 replies
sqing
Feb 18, 2025
DAVROS
4 hours ago
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Span to the infinity??
dotscom26   1
N 4 hours ago by alexheinis
The equation \[ \sqrt[3]{\sqrt[3]{x - \frac{3}{8}} - \frac{3}{8}} = x^3 + \frac{3}{8} \]has exactly two real positive solutions \( r \) and \( s \). Compute \( r + s \).
1 reply
dotscom26
Today at 9:34 AM
alexheinis
4 hours ago
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24 HMMT Guts 19 (Complex solution included)
Mathandski   2
N 4 hours ago by Adywastaken
Let $A_1 A_2 \dots A_{19}$ be a regular nonadecagon. Lines $A_1 A_5$ and $A_3 A_4$ meet at $X$. Compute $\angle A_7 X A_5$.

Complex Number Solution
2 replies
Mathandski
Feb 18, 2024
Adywastaken
4 hours ago
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No more topics!
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An inequality
JK1603JK   2
N Apr 1, 2025 by lbh_qys
Let a,b,c\ge 0: a+b+c>0 then prove \frac{a^{2}-bc}{3a+b+c}+\frac{b^{2}-ca}{3b+c+a}+\frac{c^{2}-ab}{3c+a+b}\ge 0
2 replies
JK1603JK
Mar 31, 2025
lbh_qys
Apr 1, 2025
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An inequality
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Reveal topic tags
inequalities
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JK1603JK
49 posts
JK1603JK
#1 h  Mar 31, 2025, 1:47 PM
Y by
Let a,b,c\ge 0: a+b+c>0 then prove \frac{a^{2}-bc}{3a+b+c}+\frac{b^{2}-ca}{3b+c+a}+\frac{c^{2}-ab}{3c+a+b}\ge 0
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VivaanKam
135 posts
VivaanKam
#2 h  Apr 1, 2025, 2:36 AM
Y by
Latex version.
$\text{Let } a,b,c\ge 0: a+b+c>0 \text{ then prove } \frac{a^{2}-bc}{3a+b+c}+\frac{b^{2}-ca}{3b+c+a}+\frac{c^{2}-ab}{3c+a+b}\ge 0$
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lbh_qys
549 posts
lbh_qys
#3 h  Apr 1, 2025, 2:47 AM
Y by
\[ \sum (a^2 - bc)(3b + c + a)(3c + a + b) = \sum a^2(a - b)(a - c) + 2\sum ab(a - b)^2 \geq 0. \]
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