3. If ny + 4z +3*Âťfind payz gtman tatry

1.	3. If ny + 4z +3*Âťfind payz gtman tatry
Answer» xy + yz + zx = 0 so yz = -x(y+z)x^2-yz = x(x+y+z) so 1/(x^2-yz) = 1/(x(x+y+z))similarlly1/(y^2-xz) = 1/(y(x+y+z))and1/(x^2-yz) = 1/(x(x+y+z))1/(z^2-xy) = 1/(x(x+y+z)) adding all 3 we get your expression 1/(x^2 - yz) + 1/(y^2 - zx) +1/(z^2 - xy) = 1/(x+y+z)/(1x+ 1/y + 1/z) 1/x + 1/y + 1/z = (yz+xz+xy)/xyz = 0 so1/(x^2 - yz) + 1/(y^2 - zx) +1/(z^2 - xy) = 0

Answer»

xy + yz + zx = 0

so yz = -x(y+z)x^2-yz = x(x+y+z)

so 1/(x^2-yz) = 1/(x(x+y+z))similarlly1/(y^2-xz) = 1/(y(x+y+z))and1/(x^2-yz) = 1/(x(x+y+z))1/(z^2-xy) = 1/(x(x+y+z))

adding all 3 we get your expression

1/(x^2 - yz) + 1/(y^2 - zx) +1/(z^2 - xy) = 1/(x+y+z)/(1x+ 1/y + 1/z)

1/x + 1/y + 1/z = (yz+xz+xy)/xyz = 0

so1/(x^2 - yz) + 1/(y^2 - zx) +1/(z^2 - xy) = 0

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