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1. Cho x,y>1. Tìm Min :

$P=\frac{x^{3}+y^{3}-x^{2}-y^{^{2}}}{(x-1)(y-1)}+2(x^{2}+y^{2})-16\sqrt{xy}$

2. Cho $a\neq; a,b> 0;a^{2}+2b=12$ Tìm Min: 

$P=\frac{4}{a^{4}}+\frac{4}{b^{4}}+\frac{5}{8(a-b)^{2}}$

Tìm Min:

$A=\sqrt{(x-1)^{2}+y^{2}}+\sqrt{(x+1)^{2}+y^{2}}+\left | y-2 \right |$

Cho 3 số thực dương x,y,z. Thỏa mãn: $x^{2}+y^{2}+z^{2}=xy+xz+10yz$ . Tìm GTNN của:

$P=xyz+\frac{x^{3}}{y^{2}+z^{2}}$

Cho $\left\{\begin{matrix} x,y> 0 & & \\ 2x+3y=5 & & \end{matrix}\right.$

Tìm Min: $P=\frac{\sqrt{(1+x^{2})(1+y^{2})}-1}{2y}+\frac{\sqrt{(1+x^{3})(1+y^{3})}-1}{3x^{2}}$

Bài 1: Cho a,b,c>0 : abc=1. Cm:

$\frac{1}{a^{2}-a+1}+\frac{1}{b^{2}-b+1}+\frac{1}{c^{2}-c+1}\leq 3$

Bài 2: Cho $\left\{\begin{matrix} a,b,c,d\geq 0 & & & \\ a+b+c+d=4 & & & \\ a^{2}+b^{2}+c^{2}+d^{2}=7 & & & \end{matrix}\right.$

Cm: $a^{3}+b^{3}+c^{3}+d^{3}\leq 16$

Bài 3: Cho $\left\{\begin{matrix} a,b,c,d> 0 & & \\ a^{2}+b^{2}+c^{2}+d^{2}=1 & & \end{matrix}\right.$

Cm: $\frac{1}{1-ab}+\frac{1}{1-bc}+\frac{1}{1-cd}+\frac{1}{1-da}\leq \frac{16}{3}$