Đáp án+Giải thích các bước giải:
Ta có:
`(19)/(x+y)+(19)/(z+y)+(19)/(x+z)=(133)/(10)`
`⇒19.(1/(x+y)+1/(z+y)+1/(x+z))=(133)/(10)`
`⇒1/(x+y)+1/(z+y)+1/(x+z)=(133)/(10) : 19`
`⇒1/(x+y)+1/(z+y)+1/(x+z)=7/(10)`
Ta có:
`(7z)/(x+y)+(7x)/(z+y)+(7y)/(x+z)=(133)/(10)`
`⇒7.(z/(x+y)+x/(z+y)+y/(x+z))=(133)/(10)`
`⇒z/(x+y)+x/(z+y)+y/(x+z)=(133)/(10) : 7`
`⇒z/(x+y)+x/(z+y)+y/(x+z)=19/10`
`⇒(z/(x+y)+1)+(x/(z+y)+1)+(y/(x+z)+1)=19/10+3`
`⇒(x+y+z)/(x+y)+(x+y+z)/(z+y)+(x+y+z)/(x+z)=19/10+30/10`
`⇒(x+y+z).(1/(x+y)+1/(z+y)+1/(x+z))=49/10`
`⇒(x+y+z). 7/(10)=49/10`
`⇒x+y+z=49/10 : 7/10`
`⇒x+y+z=7`
Vậy `x+y+z=7`
