Proving that: $ (a^3+b^3)^2\le (a^2+b^2)(a^4+b^4)$
66261
Inequalities help: $(a^3+b^3)^2\leq (a^2+b^2)(a^4+b^4)$
112676
Inequality $(a+b+c)(ab+bc+ca)(a^3+b^3+c^3)\le (a^2+b^2+c^2)^3$
118507
Prove $\frac{ab}{1+c^2}+\frac{bc}{1+a^2}+\frac{ca}{1+b^2}\le\frac{3}{4}$ if $a^2+b^2+c^2=1$
111267
Prove that: $2^a+3^b<3a+4b$
80009
Prove that $| |a|-|b| | \le |a-b|$
121177
Prove that $\frac{(2a+b+c)^2}{2a^2+(b+c)^2}+\frac{(2b+c+a)^2}{2b^2+(c+a)^2}+\frac{(2c+a+b)^2}{2c^2+(a+b)^2} \le 8$
152053
Proof that $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{a} \geq a+b+c$
49548
If $(a + ib)^3 = 8$, prove that $a^2 + b^2 = 4$
105641
Prove that $ab\leq\frac{1}{2\varepsilon}a^2+\frac{\varepsilon}{2}b^2$
149700
Prove that $\frac{a_1^2}{a_1+a_2}+\frac{a_2^2}{a_2+a_3}+ \cdots \frac{a_n^2}{a_n+a_1} \geq \frac12$
105164
If $abc=1$, prove that $\frac{2}{(a+1)^2+b^2+1} + \frac{2}{(b+1)^2+c^2+1} + \frac{2}{(c+1)^2+a^2+1} \le 1$.
5694
How to prove $a^2 + b^2 + c^2 \ge ab + bc + ca$?
37536
Inequality: $ab^2+bc^2+ca^2 \le 4$, when $a+b+c=3$.
58410
Simplest or nicest proof that $1+x \le e^x$
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
126018
Show that $ e^{A+B}=e^A e^B$