Minimizing $a^2+b^2+c^2+d^2$ for positive reals satisfying $(a+b) (c+d)=143$, $(a+c)(b+d)=150$, $(a+d) (b+c)=169$
134159
Smallest value of $a^2 + b^2 + c^2+ d^2$, given values for $(a+b)(c+d)$, $(a+c)(b+d)$, and $(a+d)(b+c)$
31295
$x+y\sqrt{2}$ infimum ($x,y\in \mathbb{Z}$)
15604
Determine the set of points $z$ that satisfy the condition $|2z|>|1+z^2|$
52882
find nonsingular matrices $B$ and $C$ that satisfy $BC+ CB= 0$
146254
A problem on Minima. Proving sphere has minimum surface area for a given volume
62501
Minimum value of $\frac{4}{4-x^2}+\frac{9}{9-y^2}$
56195
Find the minimum value of $\sin^{2} \theta +\cos^{2} \theta+\sec^{2} \theta+\csc^{2} \theta+\tan^{2} \theta+\cot^{2} \theta$
708
Find the minimum of $(u-v)^2+ (\sqrt{2-u^2}-\frac{9}{v})^2$ for $00$.
99692
Prove that $a^3+b^3+c^3 \geq a^2b+b^2c+c^2a$
56311
Proving $(1+a_{2})^{2}(1+a_{3})^{3}\cdots(1+a_{n})^{n}\ge n^n$ for positive reals $a_2,\ldots, a_n$ whose product is $1$
5287
Representing every positive rational number in the form of $(a^n+b^n)/(c^n+d^n)$
141529
Proving existence of a minimum
18477
$(W_1+W_2+\cdots+W_n)^a \leq W_1^a +\cdots + W_n^a$ for $n$ integer, $n\geq 2$, $W\gt 0$ and $a$ constant, real, $0\lt a\lt 1$
20055
Find minimum value of $\sum \frac{\sqrt{a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}$
54078
The minimum value of $\frac{(x+\frac{1}{x})^6-(x^6+\frac{1}{x^6})-2}{(x+\frac{1}{x})^3+x^3+\frac{1}{x^3}}$
117331
Find the minimum value of $|\sin x+\cos x+\tan x+\cot x+\sec x+\csc x|$ for real numbers $x$
87513
Global maximum and minimum of $f(x,y,z)=xyz$ with the constraint $x^2+2y^2+3z^2=6$ with Lagrange multipliers?