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Find all pairs (x,y) of real numbers such that x + y = 10 and x^2 + y^2 = 56 + xy.

 Feb 13, 2022
 #1
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Step 1:  Solve  x + y  =  10  for y:  y  =  10 - x

 

Step 2:  Replace that value for y into the equation  x2 + y2  =  56 + xy

                             --->     x2 + (10 - x)2  =  56 + x(10 - x)

 

Step 3:  Simplify that equation from step 2

 

Step 4:  Use the quadratic formula to get the two solutions.

 

Step 5:  Use those solution to get the two pairs that are the answer to the problem.

 Feb 13, 2022

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