`1/a^2+1/b^2 ≥4/(a^2+b^2)≥8/(2(a^2+b^2))≥8/(a+b)^2`
`x^2z^2+y^2z^2+1≤3z`
`⇔x^2+y^2+1/(z^2)≤3/z`
`x^2+y^2+1/z^2+1+1+4≥2x+2y+4/z`
mặt khác :
`x^2+y^2+1/z^2+1+1+4≤3/z+6`
`⇔3/z+6≥2x+2y+4/z`
`⇔6≥1/z +2x+2y`
`⇔P=1/(x+1)^2+8/(y+3)^2+(4z^2)/(1+2z)^2`
`⇔P=1/(x+1)^2+8/(y+3)^2+(1)/(1/(2z)+1)^2≥8/(x+1/(2z)+2)^2+8/(y+3)^2≥(8^2)/(x+1/(2z)+y+5)^2≥(64)/((256)/(4))≥(64)/(64)=1`
`''=''`xảy ra khi :
`x=y=1`
`z=1/2`