(x+y+z)(xy+yz+zxx)=xyz
<=>(x+y+z)(xy+yz+zx)-xyz=0
<=>3(x+y)(y+z)(z+x)=0
<=>(x+y)(y+z)(z+x)=0
<=>x=-y;y=-z;z=-x
x=-y => (-y)^2017+y^2017+z^2017=z^2017=(-y+y+z)^2017
tương tự 2 trường hợp còn lại ^_^
Các câu hỏi tương tự
\(Cho\left(x+y+z\right)\left(xy+yz+xz\right)=xyz\)
\(CMR:x^{2017}+y^{2017}+z^{2017}=\left(x+y+z\right)^{2017}\)
cho ( x +y +z)( xy +yz +xz) =xyz. CHỨNg minh rằng:
x2017 + y2017 +z2017 = (x+y+z)2017
THanks for your help!!!!!~~~~~
cho (x+y+z) (xy+yz+zx)=xyz .CMR:
x^2017+y^2017+z^2017= (x+y+z)^2017
3 tháng 10 2017 lúc 16:10
Cho \(\left(x+y+z\right)\left(xy+yz+z\right)=xyz\)
Chứng minh rằng: \(x^{2017}+y^{2017}+z^{2017}=\left(x+y+z\right)^{2017}\)
Cho x + y + z = 0 và xy + yz + xz = 0. Tính S= (x - 1)^2015 + (y - 1)^2016 + ( z + 1)^2017
cho (x + y + z)(xy + yz + zx)=xyz. Chứng minh rằng x2017 + y2017 + z2017 = (x + y +z)2017
THanks for yout help!!!!!!~
Cho xyz = 2017
CMR : \(\frac{2017x}{xy+2017x+2017}+\frac{y}{yz+y+2017}+\frac{z}{xz+z+1}=1\)
CMR: Nếu 1/x + 1/y + 1/z = 1/x+yz thì 1/x^2017 +1/y^2017 + 1/z^2017 = 1/(x^2017 + y^2017 + z^2017)
CMR nếu 1/x + 1/y + 1/z = 1/x+yz thì 1/x^2017 +1/y^2017 + 1/z^2017 = 1/(x^2017 + y^2017 + z^2017)