SOLUTION: Please help me solve this question If x2 - 2y2 = 7 and xy = 3 , find x and y Note : the number 2 behind x and 2y means squared thank you

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Question 994117: Please help me solve this question
If x2 - 2y2 = 7 and xy = 3 , find x and y
Note : the number 2 behind x and 2y means squared
thank you
Found 2 solutions by ikleyn, solver91311:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
system%28x%5E2+-+2y%5E2+=+7%2C%0D%0Axy+=+3%29.

Express y from the second equation,  y = 3%2Fx,  and substitute it into the first equation.  You will get single equation for the unknown  x:

x%5E2 - 2%283%2Fx%29%5E2 = 7.

Multiply both sides by  x%5E2.  You will get

x%5E4+-+7x%5E2+-+18 = 0.

Factor:

%28x%5E2%2B2%29%2A%28x%5E2-9%29 = 0.

The roots are  x%5E2 = -2  and  x%5E2 = 9.

The real roots are  x = +/- 3.

Correspondingly  y = +/- 1.

Answer.  The pairs  (x,y) = (3,1)  and  (x,y) = (-3,-1)  are real solutions.


Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


In the future use the caret mark (Shift-6) to indicate raising to a power. We would understand x^2 - 2y^2 = 7 to mean .









Let then,







or



Then



or



And



or



John

My calculator said it, I believe it, that settles it