Prove $a^3+b^3+c^3\geq a^2b+b^2c+c^2a$
99692
Prove that $a^3+b^3+c^3 \geq a^2b+b^2c+c^2a$
112969
Show that $ab + bc + ac \ge a\sqrt{bc} + b\sqrt{ac} + c\sqrt{ab}$
44705
Prove that $\frac{1}{a^3(b+c)}+\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)}\ge \frac32$
133428
How prove this inequality $\frac{a}{b+3}+\frac{b}{c+3}+\frac{c}{d+3}+\frac{d}{a+3}\le 1$
60073
Proving $4(a^3 + b^3) \ge (a + b)^3$ and $9(a^3 + b^3 + c^3) \ge (a + b + c)^3$
37536
Inequality: $ab^2+bc^2+ca^2 \le 4$, when $a+b+c=3$.
23080
Prove that $a^2(b+c-a)+b^2(a+c-b)+c^2(a+b-c) \leq 3abc.$
117046
Show that $\frac{a^2}{\sqrt{(1+a^3)(1+b^3)}}+\frac{b^2}{\sqrt{(1+b^3)(1+c^3)}}+\frac{c^2}{\sqrt{(1+c^3)(1+a^3)}} \geq \frac{4}{3}$
52204
Proof of one inequality $a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$
148744
Prove that $(\frac{bc+ac+ab}{a+b+c})^{a+b+c} \ge \sqrt{(bc)^a(ac)^b(ab)^c}$
95643
Proving $\sum_{cyc} \sqrt{a^2+ab+b^2}\geq\sqrt 3$ when $a+b+c=3$
63958
how to prove this inequality $(ab+bc+ac)^2 ≥ 3abc(a+b+c)$
69673
Prove that $\left (\frac{a^2 + b^2 +c^2}{a+b+c} \right) ^ {(a+b+c)} > a^a b^b c^c$
65297
Proof that for $a,b,c\in \mathbb{R}$, hold that $\left |\sqrt {a^2+b^2}-\sqrt {a^2+c^2} \right |\leq \left |b-c \right |$.
115583
prove that $a^2(p-q)(p-r)+b^2(q-p)(q-r)+c^2(r-p)(r-q)\ge 0$
15116
Proof of the inequality $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2}$
66261
Inequalities help: $(a^3+b^3)^2\leq (a^2+b^2)(a^4+b^4)$