SOLUTION: if x^2 + y^2 =36 and (x+y)^2 =64 what is the value of xy

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Question 290730: if x^2 + y^2 =36 and (x+y)^2 =64 what is the value of xy
Answer by gsmani_iyer(201) About Me  (Show Source):
You can put this solution on YOUR website!
Remember an identity %28a+%2B+b%29%5E2+=+a%5E2+%2B+2ab+%2B+b%5E2.. With this identity, we can solve the problem.
= %28x%2By%29%5E2+=+x%5E2%2B2xy%2By%5E2 or x%5E2%2By%5E2%2B2xy. whereas %28x%2By%29%5E2+=+64 ok?
But x%5E2%2By%5E2+=+36; in the above identity, we dont have the value of 2xy.
So, %28x%2By%29%5E2+-+x%5E2%2By%5E2=64-36+ which is = 28. Therefore, 2xy = 28.
So, xy = 28/2 = 14. Answer. Therefore the value of xy = 14. I hope this is clear to you. Best of luck. Feel free to contact me anytime online on any doubts in mathematics.