Question
If the sum of x , y , and z is 9, and the sum of their
squares is 18, then determine the value of the expression xy + yz + zx .Solution
(x + y + z)2Â = x2Â + y2Â + z2Â + 2(xy + yz + zx) So, 92Â = 18 + 2(xy + yz + zx) Or, 81 = 18 + 2(xy + yz + zx) So, 2(xy + yz + zx) = 81 - 18 = 63 So, (xy + yz + zx) = (63/2) = 31.5
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