ta có :
`(a-b)^2+(b-c)^2+(c-a)^2≥0`
`⇔a^2+b^2+c^2+a^2+b^2+c^2-2ab-2bc-2ac≥0`
`⇔2a^2+2b^2+2c^2≥2ab+2bc+2ac`
`⇔a^2+b^2+c^2≥ab+bc+ac=3`
`P=1/(a^2+1)+1/(b^2+1)+1/(c^2+1)`
`⇔P≥(3^2)/(a^2+b^2+c^2+3)`
`⇔P≥(3×(a^2+b^2+c^2))/2(a^2+b^2+c^2)`
`⇔P≥3/2`
`"="` xẩy ra khi :
`a=b=c=1`