If x2 + y2 + z2 + xy + y2 + zx = 0, then x +y+z is?
Answers
Answered by
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
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