query: If $x+2y+3z=10$ find the maximum value of $x^2y^2z^6$.
positive_passages.docid: 23142
positive_passages.text: Suppose $x, y, z$ are positive real number such that $x + 2y + 3z = 1$. Find the maximum value of $xyz^2$
negative_passages.docid: 70603
negative_passages.text: Finding the maximum value of a product given certain values for x,y and z
negative_passages.docid: 105768
negative_passages.text: Proof involving absolute value and maximums
negative_passages.docid: 47809
negative_passages.text: If $x,y\in\mathbb Z$, solve $x^2+xy+y^2=x^2y^2$.
negative_passages.docid: 151012
negative_passages.text: Find the value of $\lfloor x+y \rfloor$ where $x \in \mathbb{R}$, $y \in \mathbb{Z}$
negative_passages.docid: 85917
negative_passages.text: Solve $(x+1)^y-x^z=1$
negative_passages.docid: 114844
negative_passages.text: Global maxima/minima of $f(x,y,z) = x+y+z$ in $A$
negative_passages.docid: 13072
negative_passages.text: If $x,y,z\gt 0$ and $xyz=1$ Then minimum value of $\frac{x^2}{y+z}+\frac{y^2}{z+x}+\frac{z^2}{x+y}$
negative_passages.docid: 120457
negative_passages.text: Show that the equation, $x^3+10x^2-100x+1729=0$ has at least one complex root $z$ such that $|z|>12.$
negative_passages.docid: 83496
negative_passages.text: Math contest integer triplet problem: $x + y + z + xy + yz + xz = xyz − 1$
negative_passages.docid: 143194
negative_passages.text: How would you solve the diophantine $x^4+y^4=2z^2$
negative_passages.docid: 27062
negative_passages.text: Given complex $|z_{1}| = 2\;\;,|z_{2}| = 3\;\;, |z_{3}| = 4\;\;$ : when and what is $\max$ of $|z_{1}-z_{2}|^2+|z_{2}-z_{3}|^2+|z_{3}-z_{1}|^2$
negative_passages.docid: 120736
negative_passages.text: If xy + yz + zx = 1, ...........
negative_passages.docid: 87345
negative_passages.text: How many ways so that $x+y+z\leq n$?
negative_passages.docid: 146266
negative_passages.text: Find the maximum value of the expression ${\frac {x}{1+x^2}} + {\frac {y}{1+y^2}}+{\frac {z}{1+z^2}}$.
negative_passages.docid: 54078
negative_passages.text: The minimum value of $\frac{(x+\frac{1}{x})^6-(x^6+\frac{1}{x^6})-2}{(x+\frac{1}{x})^3+x^3+\frac{1}{x^3}}$
negative_passages.docid: 81063
negative_passages.text: If $p$ is a polynomial, then either $\,p(z)=z^n\,$ or $\,\max_{|z|=1}|p(z)|>1$.