How to show that $a^ab^b+a^bb^a\leq 1$ for $a,b\in(0,1)$ with $a+b=1$.
130281
Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
65280
If $a, b, c >0$ prove that $ [(1+a)(1+b)(1+c)]^7 > 7^7a^4b^4c^4 $.
93427
Show that $\sum_{i=1}^{n} \frac {a_i}{1+a-a_i} + \prod_{i=1}^{n} {(1-a_i)} \leq 1$
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
64108
how to prove $a+b-ab \le 1$ if $a,b \in [0,1]$?
25870
Prove that $0 \leq ab + ac + bc - abc \leq 2.$
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
59513
For $a, b \geq 0$, $0 < x < 1$, show $(a+b)^x \leq a^x + b^x$
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
52357
If $a,b \in G$, show that $ab^{n}a^{-1}=(aba^{-1})^{n}$.
50296
Prove $(-a+b+c)(a-b+c)(a+b-c) \leq abc$, where $a, b$ and $c$ are positive real numbers
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
14221
How can we prove it? ${a}{b}≤\frac{a^p}{p}+\frac{b^q}{q}$
148744
Prove that $(\frac{bc+ac+ab}{a+b+c})^{a+b+c} \ge \sqrt{(bc)^a(ac)^b(ab)^c}$