$a,b,c$ are positive real number..
45090
Given any positive real numbers $a,b,c$, we have $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
42567
Let $(a_n)_{n \geq 0}$ be a strictly decreasing sequence of positive real numbers , and let $z \in \mathbb C$ , $|z| < 1$.
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 $1$
54211
If $A$ and $B$ are positive definite, then is $B^{-1} - A^{-1}$ positive semidefinite?
97750
Let $a, b, c$ be positive real numbers such that $abc = 1$. Prove that $a^2 + b^2 + c^2 \ge a + b + c$.
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
16852
$|e^a-e^b| \leq |a-b|$ for complex numbers with non-positive real parts
63931
When $ab/(a+b)$ is an integer, where $a,b$ are positive integers.
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
157733
Are positive real numbers $x,y$ allowed to be taken out during this proof?
63651
If $(a,b)=1$ then there exist positive integers $x$ and $y$ s.t $ax+by=1$.
97667
If $a<b$, $c<d$ then $a+c<b+d$?
6970
If $abc=1$ and $a,b,c$ are positive real numbers, prove that ${1 \over a+b+1} + {1 \over b+c+1} + {1 \over c+a+1} \le 1$.
16140
Condition on a,b and c satisfying an equation(TIFR GS 2017)
26062
Given $a>b>2$ both positive integers, which of $a^b$ and $b^a$ is larger?
96217
If a and b are non-negative real numbers then demonstrate inequality
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.