Cho x, y, z > 0 thỏa mãn x + y + z = 1

CMR: \(\frac{1}{x^2+y^2+z^2}+\frac{1}{xyz}\ge30\)

Giải pt

\(\left(x+3\right)\sqrt{10-x^2}=x^2-x-12\)

Tính \(M=\sqrt{1+2017^2+\left(\frac{2017}{2018}\right)^2}+\frac{2017}{2018}\)

Tính \(P=\left(6+\sqrt{35}\right)\left(\sqrt{14}-\sqrt{10}\right)\sqrt{6-\sqrt{35}}\)

Giải pt

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

Cho x, y, z > 0 thỏa mãn x + y +z = xy + yz + zx

CMR \(\frac{1}{x^2+y+1}+\frac{1}{y^2+z+1}+\frac{1}{z^2+x+1}\le1\)

Cho a; b; c > 0 thỏa mãn ab + bc + ca = 3

CMR \(\frac{1}{a^2+b^2+1}+\frac{1}{b^2+c^2+1}+\frac{1}{c^2+a^2+1}\le1\)