Question

If x2 + y2 + z2 = 20 and x + y + z = 0, then xy + yz + zx is equal to :

Answer 1

Hi friend
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Your answer
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Given that : - (x² + y² + z²) = 20 and (x + y + z) = 0

To find : - Value of (xy + yz + zx) .

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

Now, putting the values , we get,

(0)² = 20 + 2 (xy + yz + zx)

=> 2(xy + yz + zx) = 0 - 20

=> (xy + yz + zx ) = - 20/2

=> xy + yz + zx = - 10

HOPE IT HELPS