How much is the minimum of $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$
13220
find the minimum value of $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$
103744
Minimal $ab$ for Rational Number $a/b$ in an Interval
141529
Proving existence of a minimum
52305
Is there a general relation between $a/b$ and $(a+c)/(b+c)$ where $a,b,c > 0 $?
154716
Prove $\frac{1}{a^3+b^3+abc}+\frac{1}{a^3+c^3+abc}+\frac{1}{b^3+c^3+abc} \leq \frac{1}{abc}$
155493
Minimum value of the expression given below.
82317
Find the minimum value of $A=\frac{2-a^3}{a}+\frac{2-b^3}{b}+\frac{2-c^3}{c}$
23694
Given that $abc=1$, prove that $\frac{b}{c} + \frac{c}{a}+ \frac{a}{b} \ge \frac{1}{a} + \frac{1}{b} +\frac{1}{c}$.
56101
Prove the inequality $\frac{a}{c+a-b}+\frac{b}{a+b-c}+\frac{c}{b+c-a}\ge{3}$
112565
Prove that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\geq \frac{9}{a+b+c} : (a, b, c) > 0$
62501
Minimum value of $\frac{4}{4-x^2}+\frac{9}{9-y^2}$
26617
Minimum value of $ f(x,y,z)=\left(x+\frac{1}{y}\right)^2+\left(y+\frac{1}{z}\right)^2+\left(z+\frac{1}{x}\right)^2. $
29424
Maximum value of $\sin A+\sin B+\sin C$?
52204
Proof of one inequality $a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$
137105
The minimum value of $x^8 – 8x^6 + 19x^4 – 12x^3 + 14x^2 – 8x + 9$ is
15730
Determine the minimum of $a^2 + b^2$ if $a,b\in\mathbb{R}$ are such that $x^4 + ax^3 + bx^2 + ax + 1 = 0$ has at least one real solution
140001
Minimum value of $2^{\sin^2x}+2^{\cos^2x}$