Let $a$ and $b$ be two real positive numbers. Show that $a+b+\frac{1}{1+ \sqrt{ab}} \ge \frac{5}{2}$.
133382
Proof that $a+b+\frac{1}{1+\sqrt{ab}}\geq\frac{5}{2}$
138216
$a,b,c$ are positive real numbers such that, $a+b+c\ge abc$. Prove that $a^2+b^2+c^2\ge \sqrt{3}abc$
50296
Prove $(-a+b+c)(a-b+c)(a+b-c) \leq abc$, where $a, b$ and $c$ are positive real numbers
130281
Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
126018
Show that $ e^{A+B}=e^A e^B$
5694
How to prove $a^2 + b^2 + c^2 \ge ab + bc + ca$?
7491
How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
44705
Prove that $\frac{1}{a^3(b+c)}+\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)}\ge \frac32$
101362
Let a,b,c be positive real number, proof.
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
1275
Prove that $a_1+\cdots+a_n \geq n$ if $a_1$, $a_2$, ... $a_n$ are positive real numbers and their product is $1$
63958
how to prove this inequality $(ab+bc+ac)^2 ≥ 3abc(a+b+c)$
150581
How do I show that $\frac a{1 - a^2} + \frac b{1 - b^2} + \frac c{1 - c^2} \ge \frac {3 \sqrt 3}2$
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 $1$
97750
Let $a, b, c$ be positive real numbers such that $abc = 1$. Prove that $a^2 + b^2 + c^2 \ge a + b + c$.
29342
Prove the inequality: $(y+z)*x^4+(x+z)*y^4+(x+y)*z^4\le((x+y+z)^5)/12$ for positive reals.