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Mathematics
Word Shallow's user avatar
Word Shallow's user avatar
Word Shallow's user avatar
Word Shallow
  • Member for 7 years, 5 months
  • Last seen more than 2 years ago
  • google.com
  • Kamihimekawa Bridge, Otobe, Hokkaido, Japan
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Apparently, this user prefers to keep an air of mystery about her. :)

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View all questions and answers
7
For $\Delta ABC$ right-angled triangle at $A$ have $AB=AC$. Calculate the ratio of $MA: MB: MC$
Jun 3, 2017
5
Find the number of ordered triplets satisfying $5\left(x+\frac{1}{x}\right)=12\left(y+\frac{1}{y}\right)=13\left(z+\frac{1}{z}\right)$
Mar 3, 2019
5
Brocard's theorem - $O$ is orthocenter of $\Delta EFI$
Feb 20, 2019
4
Given the positive numbers $a, b, c$. Prove that $\frac{a}{\sqrt{a^2+1}}+\frac{b}{\sqrt{b^2+1}}+\frac{c}{\sqrt{c^2+1}}\le \frac{3}{2}$
Feb 14, 2017
4
For $x,y,z>0$. Minimize $P=\frac{1}{4x^{2}-yz+2}+\frac{1}{4y^{2}-zx+2}+\frac{1}{4z^{2}-xy+2}$
Feb 25, 2017
4
Prove this inequality $3(abc+4)\ge 5(ab+bc+ca)$
Sep 21, 2017
4
minimum of $a^2+4b^2+c^2$ given $2a+b+3c=20$
Mar 26, 2019
4
Prove that $\sum_{cyc}\sqrt{a^2+\frac{1}{\left(b+1\right)^2}}\ge \frac{\sqrt{181}}{5}$
Jun 6, 2017
4
Prove inequality $a<1<b<3<c<4$
Jun 1, 2017
3
Prove this inequality $\sum_{cyc}\frac{x+y}{4+yz}\ge \frac{3}{2}$
Nov 17, 2017