Find the maximum of $\frac{x}{1+yz}+\frac{y}{1+xz}+\frac{z}{1+xy}$, where $0\leq x,y,z\leq 1$.
77777
If $0\le a,b,c\le 1$, then $\frac a{1+bc}+\frac b{1+ac}+\frac c{1+ab}\le 2$
13220
find the minimum value of $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$
136586
Making $x+\frac1y$, $y+\frac1z$, and $z+\frac1x$ all integer.
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
34325
Minimizing $\sum_{i=1}^n \max(|x_i - x|, |y_i - y|)$ - Sum of Max of Absolute Values
31257
Let $a,b,c>0$ such that $a+b+c=3$, find max/min of $\frac1{a^2+1}+\frac1{b^2+1}+\frac1{c^2+1}$
45616
Find all solutions of ${\frac {1} {x} } + {\frac {1} {y} } +{\frac {1} {z}}=1$, where $x$, $y$ and $z$ are positive integers
13072
If $x,y,z\gt 0$ and $xyz=1$ Then minimum value of $\frac{x^2}{y+z}+\frac{y^2}{z+x}+\frac{z^2}{x+y}$
6595
Solve for positive integers: $\frac{4}{13}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$
145152
How to prove that $\frac{x^2}{yz+2}+\frac{y^2}{zx+2}+\frac{z^2}{xy+2}\geq \frac{x+y+z}{3}$ holds for any $(x,y,z)\in[1,2]^3$
45439
Given reals $a_1, a_2, \cdots, a_{n - 1}, a_n$ such that $\sum_{i = 1}^na_1^2 = 1$. Calculate the maximum value of $\sum_{cyc}|a_1 - a_2|$.
89170
How prove this inequality $\frac{x^2y}{z}+\frac{y^2z}{x}+\frac{z^2x}{y}\ge x^2+y^2+z^2$
68990
Show that $\frac 1{1+x+y^{-1}}+\frac1{1+y+z^{-1}}+\frac1{1+z+x^{-1}}=1$ if $xyz=1$
137919
How do I find $\lim_{(x,y) \to (0,0)} \frac{\sqrt{xy + 1} -1}{x + y}$?
76441
Max. and Min. value of $|z|$ in $\left|z+\frac{2}{z}\right| = 2\,$
79125
How to find the maximum value for the given $x\cos{\lambda}+y\sin{\lambda}$?
121362
If $A,B>0$ and $A+B = \frac{\pi}{3},$ Then find Maximum value of $\tan A\cdot \tan B$.