SOLUTION: If x+y+z=12,x2+y2+z2=64,find xy+yz+zx

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Question 1037398: If x+y+z=12,x2+y2+z2=64,find xy+yz+zx
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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If x+y+z=12, x2+y2+z2=64, find xy+yz+zx
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Use  %28x%2By%2Bz%29%5E2 - %28x%5E2+%2B+y%5E2+%2Bz%5E2%29 = 2%2A%28xy%2Byz%2Bzx%29.


It gives  12%5E2 - 64 = 2%2A%28xy%2Byz%2Bzx%29,  or


xy%2Byz%2Bzx = %28144-64%29%2F2 = 40.


Answer.  40.