Question

This is the best question for all brainly members.

Answer 1

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=>x²+y²+z²-xy-yz-zx =0

Now both sides multiply by 2

=>2(x²+y²+z²-xy-yz-zx) = 0×2

=>2x²+2y²+2z²-2xy-2yz-2zx=0

=>(x²+2xy+y²)+(y²+2yz+z²)+(z²+2zx+x²) = 0


=>(x-y)²+(y-z)²+ (z-x)²= 0

=>(x-y)=0 (y-z)=0 (z-x)=0

•••Then x=y=z........ Proved.

Answer 2

Given Equation is x^2 + y^2 + z^2 - xy - yz - zx = 0.

Multiply the equation with 2 on both sides, we get

2(x^2 + y^2 + z^2 - xy - yz - zx) = 0 * 2

2x^2 + 2y^2 + 2z^2 - 2xy - 2yz - 2zx = 0

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

(x - y)^2 + (y - z)^2 + (z - x)^2 = 0

(x - y) = 0, (y - z) = 0, (z - x) = 0

x = y, y = z, z = x

x = y = z


Hope this helps!