Question

If x² +y²+z²-xy-yz-zx=0 value of (x+y)/2 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 Ans.