Question

If x2 + y2 + z2 + xy + y2 + zx = 0, then x +y+z is?
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Answer 1

Step-by-step explanation:

Given x

2

+y

2

+z

2

−xy−yz−zx=0

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=z=k

⇒

z

x+y

=

k

2k

=2