How to easily prove $x+\frac{1}{x} \ge 2 \quad ∀x\in ℝ^+$
44233
How to prove this inequality $ x + \frac{1}{x} \geq 2 $
66902
Prove that $\int_{-\infty}^{\infty} \frac{e^{2x}-e^x}{x (1+e^{2x})(1+e^{x})}\mathrm{d}x=\log 2$
105641
Prove that $ab\leq\frac{1}{2\varepsilon}a^2+\frac{\varepsilon}{2}b^2$
51653
Prove that $m+\frac{4}{m^2}\geq3$ for every $m > 0$
14763
How to prove $\frac{1}{4}(\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{d}+\frac{d^2}{a})\ge \sqrt[4]{\frac{a^4+b^4+c^4+d^4}{4}}$
48503
Proving : $ \bigl(1+\frac{1}{n+1}\bigr)^{n+1} \gt (1+\frac{1}{n})^{n} $
99676
Prove $\sum{\frac{1}{(x+2y)^2}} \geq\frac{1}{xy+yz+zx}$
12020
Prove $\sqrt{n+1}-\sqrt{n}\lt \frac{1}{2\sqrt{n}}$
100995
For what $x$ : $2\sqrt{x}+\dfrac{1}{\sqrt{x+1}} \leq 2\sqrt{x+1}$
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
44438
Prove : $\frac{\cos(x_1) +\cos(x_2) +\cdots+\cos(x_{10})}{\sin(x_1) +\sin(x_2) +\cdots+\sin(x_{10})} \ge 3$
58041
Prove by Mean Value Theorem $\frac{x}{1+x}0$
1305
Proving the AM-GM inequality for 2 numbers $\sqrt{xy}\le\frac{x+y}2$
150581
How do I show that $\frac a{1 - a^2} + \frac b{1 - b^2} + \frac c{1 - c^2} \ge \frac {3 \sqrt 3}2$
18606
How prove $\frac{a^2}{a+2b^2}+\frac{b^2}{b+2c^2}+\frac{c^2}{c+2a^2}\ge 1$
111847
For $a,b,c>0$, prove that $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge a+b+c+\frac{4(a-b)^2}{a+b+c}$
124968
How prove this inequality $\sum\limits_{cyc}\frac{x+y}{\sqrt{x^2+xy+y^2+yz}}\ge 2+\sqrt{\frac{xy+yz+xz}{x^2+y^2+z^2}}$