SOLUTION: x^2+y^2=113 xy=56 what are the soultions?

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Question 1085675: x^2+y^2=113
xy=56
what are the soultions?
Found 3 solutions by Alan3354, josgarithmetic, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+y^2=113
xy=56
what are the soultions?
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Just by observation:
7^2 + 8^2 = 113
7*8 = 56
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(-7)^2 + (-8)^2 = 113
-7*(-8) = 56

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
xy=56

y=56%2Fx

Substitute into the other equation.
x%5E2%2B%2856%2Fx%29%5E2=113

x%5E4%2B56%5E2=113x%5E2

x%5E4-113x%5E2%2B56%5E2=0

discriminant, 113%5E2-4%2A56%5E2=225=15%5E2

x%5E2=%28113%2B-+15%29%2F2, notice this is for x%5Ehighlight_green%282%29.

system%28x%5E2=49%2COR%2Cx%5E2=64%29,..... which will give that the combinations of solutions are the numbers 7 and 8. As example, x=7 and y=8; or x=-7 and y=-8.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.


Curves x%5E2+%2B+y%5E2 = 113 and xy = 56.


On solving systems of non-linear equations see the lessons
    - Solving algebraic equations of high degree
    - Solving the system of algebraic equations of degree 2 and degree 1
    - Solving the system of algebraic equations of degree 2
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of equations that are not linear".