SOLUTION: If x+y+z=7 and x^2+y^2+z^2=19, then what is the arithmetic mean (average) of the three products xy, yz, and zx?

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Question 1023639: If x+y+z=7 and x^2+y^2+z^2=19, then what is the arithmetic mean (average) of the three products xy, yz, and zx?
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
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If x+y+z=7 and x^2+y^2+z^2=19, then what is the arithmetic mean (average) of the three products xy, yz, and zx?
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The key to solving this problem is this identity

 =  + .

It implies that 

 =  = 15.

Then  =  = 5.

It is your answer.


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