Show that for all $a,b,c$ positive real numbers that $(a+b+c)(a^{-1}+b^{-1}+c^{-1})\geq 9$
15599
Given that a,b,c are distinct positive real numbers, prove that (a + b +c)( 1/a + 1/b + 1/c)>9
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
130281
Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
88687
Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
82097
If $A \succeq B$, is it true that $B^{-1} \succeq A^{-1}$?
59513
For $a, b \geq 0$, $0 < x < 1$, show $(a+b)^x \leq a^x + b^x$
72313
Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$
11127
Let $a$, $b$, and $c$ be positive real numbers.
158844
If $a$ and $b$ are positive real numbers such that $a+b=1$, prove that $(a+1/a)^2+(b+1/b)^2\ge 25/2$
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
55266
Prove that $(n+1)^{n-1}<n^n$
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
23869
Prove the implication "if $ac>bc$ and $c>0$, then $a>b$" using the contrapositive
11868
Let $a,b,c\in \Bbb R^+$ such that $(1+a+b+c)(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=16$. Find $(a+b+c)$
141102
If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.
49217
How do I show that $a^p + b^p > (a + b)^p$ for $a,b>0$ and $0<p<1$?