Prove inequality $(1+x+y)(1+y+z)(1+z+x) \ge 9(xy+xz+yz)$
60122
Prove $(1+a+b)(1+b+c)(1+c+a)\ge 9(ab+bc+ca)$
143968
Proving this inequality by mathematical induction
152311
Proving expression$\geq 2$, where variables are $x,y,z$
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
56623
Stuck trying to prove an inequality
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
33903
Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
95852
Prove that $(a+b)(b+c)(c+a) \ge8$
121107
Proof by induction: $n^{n+1} > (n + 1)^n$, $(1 + x)^n \ge 1 + nx$, other inequalities
66996
Proof by induction of Bernoulli's inequality $ (1+x)^n \ge 1+nx$
66707
How to prove this inequality? $ | z-1 | \le | | z | -1 | + | z| \cdot | \arg z | $
105047
Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$
27570
Prove $(1-x)\ln(1-x)+(1+x)\ln(1+x)\leq 2x^2$ for $0<x<1$
27911
How can I prove that $xy\leq x^2+y^2$?
126557
Proving the inequality $\sum_{\text{cyc}} \frac{a}{a^2+b^3+c^3}\le\frac1{5abc}$
5465
This inequality $a+b^2+c^3+d^4\ge \frac{1}{a}+\frac{1}{b^2}+\frac{1}{c^3}+\frac{1}{d^4}$