query: Find the maximum value of $a^2b^3$ where $a,b$ are positive real numbers satisfying $a+b=10$
positive_passages.docid: 144512
positive_passages.text: Find the greatest value of $a^2\cdot b^3$ where $a+b=10$
negative_passages.docid: 34325
negative_passages.text: Minimizing $\sum_{i=1}^n \max(|x_i - x|, |y_i - y|)$ - Sum of Max of Absolute Values
negative_passages.docid: 19402
negative_passages.text: Find integral solution of $a^{b} - b^{a} = 3$
negative_passages.docid: 127032
negative_passages.text: Maximum of $\cos \alpha_{1}\cdot \cos \alpha_{2}\cdot \cos \alpha_{3}....\cos \alpha_{n}.$
negative_passages.docid: 156541
negative_passages.text: $a^b > b^a$ or $a^b b$ where $a,b$ are positive real numbers
negative_passages.docid: 121362
negative_passages.text: If $A,B>0$ and $A+B = \frac{\pi}{3},$ Then find Maximum value of $\tan A\cdot \tan B$.
negative_passages.docid: 125057
negative_passages.text: How do I solve a problem with term $a^{n} + b^{n}$?
negative_passages.docid: 41619
negative_passages.text: How find the maximum value of $|bc|$
negative_passages.docid: 99055
negative_passages.text: How find this $x^3-5x+10=2^y$
negative_passages.docid: 79125
negative_passages.text: How to find the maximum value for the given $x\cos{\lambda}+y\sin{\lambda}$?
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: 141183
negative_passages.text: How to determine highest power of $2$ in $3^{1024}-1$?
negative_passages.docid: 74222
negative_passages.text: If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
negative_passages.docid: 72360
negative_passages.text: Find the value of $a^{2m}+a^m+{1\over a^m}+{1\over a^{2m}}$
negative_passages.docid: 55100
negative_passages.text: The positive integer solutions for $2^a+3^b=5^c$
negative_passages.docid: 88580
negative_passages.text: Finding the maximum value of $\int_0^1 f^3(x)dx$
negative_passages.docid: 115719
negative_passages.text: Find the possible values of |A + B + C |