[administration]

If x² + y² + z² = 4, and k=xy+yz+zx, then
A) k>= -2
B) k<= -4
C) k<= -2
D) k>= -4

[Wonder Boy]

We know that (x + y + z)² = x² + y² + z² + 2(xy + yz + zx)

–> 2(xy + yz + zx) = (x + y + z)² – ( x² + y² + z² )

–> 2(xy + yz + zx) = (x + y + z)² – 4

since (x + y + z)² >= 0

so, 2(xy + yz + zx) >= 0-4 –> (xy + yz + zx) >= -2  -> k>=-2

[Author]

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