SOLUTION: if x+y+z=20, and x^2+y^2+z^2=100, then what is the value of xy+xz+yz?

Algebra ->  Finance -> SOLUTION: if x+y+z=20, and x^2+y^2+z^2=100, then what is the value of xy+xz+yz?      Log On


   

Question 1129212: if x+y+z=20, and x^2+y^2+z^2=100, then what is the value of xy+xz+yz?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Use an identity


    %28x%2By%2Bz%29%5E2 = x%5E2+%2B+y%5E2+%2B+z%5E2+%2B+2xy+%2B+2xz+%2B+2yz.


Substitute the given data. You will get


    20%5E2 = 100 + 2*(xy + xz + yz),


which implies


    xy + xz + yz = %28400-100%29%2F2 = 300%2F2 = 150.     ANSWER


Answer.  The value of  xy + xz + yz  is equal to  150.

Solved.