Question

if x² + y²+ z²- xy+ yz+ zx = 0 then x+y/z is

Answer 1

X²+y²+z²-xy-yz-zx=0
or, 2x²+2y²+2z²-2xy-2yz-2zx=0
or, (x²-2xy+y²)+(y²-2yz+z²)+(z²-2zx+x²)=0
or, (x-y)²+(y-z)²+(z-x)²=0
or, (x-y)²=0, (y-z)²=0, (z-x)²=0
or, x-y=0, y-z=0, z-x=0
or, x=y, y=z, z=x
or, x=y=z=k (say)
∴, (x+y)/z
=(k+k)/k
=2k/k
=2