SOLUTION: If x + y = 4 and xy = -12; what is the value of x^2 + 5xy + y^2?

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Question 1132819: If x + y = 4 and xy = -12; what is the value of x^2 + 5xy + y^2?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


x%5E2%2B5xy%2By%5E2+=+%28x%5E2%2B2xy%2By%5E2%29%2B3xy+=+%28x%2By%29%5E2%2B3xy

Evaluate using the given values of (x+y) and (xy).

Answer by ikleyn(52834) About Me  (Show Source):
You can put this solution on YOUR website!
.

  x^2 + 5xy + y^2 = (x^2 + 2xy + y^2) + 3xy = (x+y)^2 + 3xy = 


        now substitute x+y = 4 and xy = -12 to get


= 4%5E2+%2B3%2A%28-12%29 = 16 - 36 = -20.       ANSWER

Solved.