How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
30386
Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
96327
Show that $a^x+b^x+c^x>(a+b+c)^x$ for all $a,b,c>0$ and $0<x<1$
40700
Proving inequality $(a+\frac{1}{a})^2 + (b+\frac{1}{b})^2 \geq \frac{25}{2}$ for $a+b=1$
66707
How to prove this inequality? $ | z-1 | \le | | z | -1 | + | z| \cdot | \arg z | $
130281
Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
89175
Proof of $(a+b)^{n+1}$
145884
Showing $\left|\frac{a+b}{2}\right|^p+\left|\frac{a-b}{2}\right|^p\leq\frac{1}{2}|a|^p+\frac{1}{2}|b|^p$
15232
Proving an inequality involving real powers
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
91617
Prove this inequality $a \sqrt{1-b^2}+b\sqrt{1-a^2}\le1 $
63958
how to prove this inequality $(ab+bc+ac)^2 ≥ 3abc(a+b+c)$
17601
How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
50266
In the following figure prove that: $AK||BC$
77026
Proof with inequalities
56315
Prove $\frac{|a+b|}{1+|a+b|}<\frac{|a|}{1+|a|}+\frac{|b|}{1+|b|}$.
130327
Prove that $a^2 > b^2$ ; if $a > b \geq 0$.