Evaluate the product xy , given x^2 + y^2 = 34 and x + y = 8

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Stackexchange user Git Gud posed this question October 10, 2016. The problem solver was to find the value of xy given x^2 + y^2 = 34 and x + y = 8. One approach is to directly find the values of x and y as intersection points of a circle and line. Then multiply the coordinates together to obtain the product xy. A more elegant and clever solution is presented here where xy can be found without finding the values of x and y individually!

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