if x2+y2+z2-xy-yz-zx=0,then find (x+y)/z.
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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.
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.
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