SOLUTION: which of the following is a step in the solution of the given equations? x^2+y^2=65 (1/2)xy=14 a. x+y=121 b.x^2-11x+28=0 c.x^2+2xy+y^2=79 d.11+-(121+112)^(1/2) ----------- -

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: which of the following is a step in the solution of the given equations? x^2+y^2=65 (1/2)xy=14 a. x+y=121 b.x^2-11x+28=0 c.x^2+2xy+y^2=79 d.11+-(121+112)^(1/2) ----------- -      Log On


   

Question 145093: which of the following is a step in the solution of the given equations?
x^2+y^2=65
(1/2)xy=14
a. x+y=121
b.x^2-11x+28=0
c.x^2+2xy+y^2=79
d.11+-(121+112)^(1/2)
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2
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
If you try to solve by completing the square, you'll see that in order to get
x%5E2%2By%5E2=65 to be a square on the left hand side, you'll need to add
%282%29xy on both sides. And we are given as %281%2F2%29xy=14
So
x%5E2%2By%5E2=65
x%5E2%2B2xy%2By%5E2=65+%2B+2xy
x%5E2%2B2xy%2By%5E2=65+%2B+4%2A%281%2F2%29xy
x%5E2%2B2xy%2By%5E2=65+%2B+4%2A14
%28x+%2B+y%29%5E2+=+121
%28x+%2B+y%29+=+sqrt%28121%29
(x + y) = (+-)11
I don't see that as any of your choices :(