SOLUTION: If x + y = 11 and y = 15/x, find the value of x^2 + y^2.

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Question 256387: If x + y = 11 and y = 15/x, find the value of x^2 + y^2.
Found 2 solutions by Edwin McCravy, jim_thompson5910:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
If x+%2B+y+=+11 and y+=+15%2Fx, find the value of x%5E2+%2B+y%5E2.


x%2By=11
square both sides:
%28x%2By%29%5E2=11%5E2
x%5E2%2B2xy%2By%5E2=121
x%5E2%2By%5E2=121-2xy

Take the other equation

y+=+15%2Fx
Multiply both sides by x
xy=15
Substitute 15 for xy in

x%5E2%2By%5E2=121-2xy
x%5E2%2By%5E2=121-2%2815%29
x%5E2%2By%5E2=121-30
x%5E2%2By%5E2=91

Edwin

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
One way you could do it is to explicitly solve for both x and y and then just add their squares. However, here's another way to do this problem.


y+=+15%2Fx Start with the second equation.


xy+=+15 Multiply both sides by x.


2xy+=+30 Multiply both sides by 2.


x+%2B+y+=+11 Move back to the first equation.


%28x+%2B+y%29%5E2+=+%2811%29%5E2 Square both sides


%28x+%2B+y%29%5E2+=+121 Square 11 to get 121


x%5E2%2B2xy%2By%5E2+=+121 FOIL


x%5E2%2B30%2By%5E2+=+121 Plug in 2xy+=+30 (this is why I manipulated the second equation)


x%5E2%2By%5E2+=+121-30 Subtract 30 from both sides.


x%5E2%2By%5E2+=+91 Subtract


So the solution is x%5E2%2By%5E2+=+91