\(x+y+z=0\)
=>\(\left(x+y+z\right)^2=0\)
=>\(x^2+y^2+z^2+2xy+2yz+2xz=0\)
=>\(x^2+y^2+z^2+2\left(xy+yz+xz\right)=0\)
=>\(2+2\left(xy+yz+xz\right)=0\)
=>\(xy+yz+xz=-1\)
=>\(\left(xy+yz+xz\right)^2=1\)
=>\(x^2y^2+y^2z^2+x^2z^2+2xy^2z+2xyz^2+2x^2yz=1\)
=>\(x^2y^2+y^2z^2+x^2z^2+2xyz\left(y+z+x\right)=1\)
=>\(x^2y^2+y^2z^2+x^2z^2+2.xyz.0=1\)
=>\(x^2y^2+y^2z^2+x^2z^2=1\)
Mặt khác: \(x^2+y^2+z^2=2\)
=>\(\left(x^2+y^2+z^2\right)^2=4\)
=>\(x^4+y^4+z^4+2x^2y^2+2y^2z^2+2x^2z^2=4\)
=>\(x^4+y^4+z^4+2\left(x^2y^2+y^2z^2+x^2z^2\right)=4\)
=>\(x^4+y^4+z^4+2.1=4\)
=>\(x^4+y^4+z^4+2=4\)
=>\(x^4+y^4+z^4=2\)
minh nghi ban nen dung dau tuong duong Tra My
