query: find the maximum value of $xy + yz +zx$
positive_passages.docid: 22528
positive_passages.text: maximum value of $xy+yz+zx.$ given $x+2y+z=4$
negative_passages.docid: 11824
negative_passages.text: A maximization problem
negative_passages.docid: 56796
negative_passages.text: Maximum of $x^3+y^3+z^3$ with $x+y+z=3$
negative_passages.docid: 69465
negative_passages.text: Get the maximum value from an element in a multidimensional array?
negative_passages.docid: 149269
negative_passages.text: If $a,b,c,d,e,f$ are non negative real numbers such that $a+b+c+d+e+f=1$, then find maximum value of $ab+bc+cd+de+ef$
negative_passages.docid: 49209
negative_passages.text: Prove $(x+y)(y+z)(x+z)≤\frac8{27}(x+y+z)^3$
negative_passages.docid: 58629
negative_passages.text: Show that the $\max{ \{ x,y \} }= \frac{x+y+|x-y|}{2}$.
negative_passages.docid: 25203
negative_passages.text: with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$
negative_passages.docid: 96127
negative_passages.text: Maximum of $|\sin(z)|$ as $\{z: |z| \leq 1 \} $
negative_passages.docid: 99676
negative_passages.text: Prove $\sum{\frac{1}{(x+2y)^2}} \geq\frac{1}{xy+yz+zx}$
negative_passages.docid: 18313
negative_passages.text: show this inequality with $xy+yz+zx=3$
negative_passages.docid: 31257
negative_passages.text: Let $a,b,c>0$ such that $a+b+c=3$, find max/min of $\frac1{a^2+1}+\frac1{b^2+1}+\frac1{c^2+1}$
negative_passages.docid: 87907
negative_passages.text: How to find the maximum and minimum value of $\left|(z_1-z_2)^2 + (z_2-z_3)^2 + (z_3-z_1)^2\right|$ (where $|z_1|=|z_2|=|z_3|=1$)?
negative_passages.docid: 114996
negative_passages.text: $x+y+z=n$. Finding the number of solutions.
negative_passages.docid: 83496
negative_passages.text: Math contest integer triplet problem: $x + y + z + xy + yz + xz = xyz − 1$
negative_passages.docid: 155341
negative_passages.text: Proving or disproving inequality $ \frac{xy}{z} + \frac{yz}{x} + \frac{zx}{y} \ge x + y + z $
negative_passages.docid: 81790
negative_passages.text: Polynomial maximization: If $x^4+ax^3+3x^2+bx+1 \ge 0$, find the maximum value of $a^2+b^2$