xin hay nhất cố làm có tâm lắm rồi :v
ý tưởng :
ta có :`3x+2y+3z=(x+y)+(y+z)+2(x+z)`
và `3x+2y+3z=2(x+y)+(x+3z)=2(y+z)+(z+3x)=(4y+6(x+z))/2`
ta có :
`P=(x+3z)/(x+y)+(z+3x)/(y+z)+(4y)/(x+z)`
`⇔10+P=((x+3z)/(x+y)+2)+((z+3x)/(y+z)+2)+((4y)/(x+z)+6)`
`⇔10+P=(x+3z+2(x+y))/(x+y)+(z+3x+2(y+z))/(y+z)+(4y+6(x+z))/(x+z)`
`⇔10+P=(3x+2y+3z)/(x+y)+(3x+2y+3z)/(y+z)+(2(3x+2y+3z))/(x+z)`
`⇔10+P=(3x+2y+3z)(1/(x+y)+1/(y+z)+2/(x+z))`
`⇔10+P=((x+y)+(y+z)+2(x+z))(1/(x+y)+1/(y+z)+2/(x+z))`
theo `bu-nhi-a`
`⇔10+P≥(1.1+1.1+√2.√2)^2`
`⇔10+P≥16`
`⇔P≥6`
`''=''`xẩy ra khi :
`x=y=z`
