\(\text{Cho x,y,z }\in R\text{ thỏa mãn điều kiện }xyz=1\text{.Tìm Min:}\)

\(P=\left(\left|xy\right|+\left|yz\right|\left|zx\right|\right).\left[15\sqrt{x^2+y^2+z^2}-7\left(x+y-z\right)\right]+1\)

\(Cho\text{ }x,y,z\text{ }\in R\text{ thỏa}\text{ }xyz=1.\text{Tìm Min:}\)

\(P=\left(\left|xy\right|+\left|yz\right|+\left|zx\right|\right)\left[15\sqrt{x^2+y^2+z^2}-7\left(x+y-z\right)\right]+1\)

\(\text{Cho a,b,c đôi một khác nhau}.\text{Chứng minh:}\)

\(P=\dfrac{a^2+b^2}{\left(a-b\right)^2}+\dfrac{b^2+c^2}{\left(b-c\right)^2}+\dfrac{c^2+a^2}{\left(c-a\right)^2}\ge\dfrac{5}{2}\)

\(\sqrt{2x^2-1}+\sqrt{x^2-3x-2}=\sqrt{2x^2+2x+3}+\sqrt{x^2-x+2}\)