Prove that $a^2(1+b^4)+b^2(1+a^4)≤(1+a^4)(1+b^4)$
118517
Does this constitute a valid proof that $\frac{x^2}{1+x^4} \leq \frac{1}{2}$?
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
88687
Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
14763
How to prove $\frac{1}{4}(\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{d}+\frac{d^2}{a})\ge \sqrt[4]{\frac{a^4+b^4+c^4+d^4}{4}}$
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
1478
An inequality for powers of reals: $a^{1/n}-b^{1/n}<(a-b)^{1/n}$
63958
how to prove this inequality $(ab+bc+ac)^2 ≥ 3abc(a+b+c)$
117046
Show that $\frac{a^2}{\sqrt{(1+a^3)(1+b^3)}}+\frac{b^2}{\sqrt{(1+b^3)(1+c^3)}}+\frac{c^2}{\sqrt{(1+c^3)(1+a^3)}} \geq \frac{4}{3}$
8207
Can I prove this inequality algebraically?
12837
Inequality with condition $x^2+y^2+z^2=1$.
25258
Prove that if $ a,b,c > 0 $, then $ [(1 + a) (1 + b) (1 + c)]^{7} > 7^{7} (a^{4} b^{4} c^{4}) $.
136403
Prove that $\sqrt{a}\leq\frac{1+a}{2}$
29462
Suggestions on how to prove the following equality. $a^{m+n}=a^m a^n$
84946
If $0<a<b$, prove that $a<\sqrt{ab}<\frac{a+b}{2}<b$
44247
For $a^3+b^3+c^3=3$ prove that $a^4b+b^4c+c^4a\leq3$
96327
Show that $a^x+b^x+c^x>(a+b+c)^x$ for all $a,b,c>0$ and $0<x<1$
97057
Show $a^2+b^2+c^2=1$ $\implies$ $ \dfrac {b^2c^2}{1+a^2} +\dfrac {c^2a^2}{1+b^2}+\dfrac {a^2b^2}{1+c^2} \le \dfrac 14 $