SOLUTION: It says to solve this nonlinear system: x=y^2 and y=x^2
I'm not sure if it's easy and I'm having a dumb moment but I really would like to understand how to solve this question. Th
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-> SOLUTION: It says to solve this nonlinear system: x=y^2 and y=x^2
I'm not sure if it's easy and I'm having a dumb moment but I really would like to understand how to solve this question. Th
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Question 518461: It says to solve this nonlinear system: x=y^2 and y=x^2
I'm not sure if it's easy and I'm having a dumb moment but I really would like to understand how to solve this question. Thank you! Answer by solver91311(24713) (Show Source):
Not exactly trivial. There is more to it than meets the eye at first glance.
Substitute the first into the second:
which is to say:
Which is a quartic equation demanding that we find 4 roots over the complex numbers. (The Fundamental Theorem of Algebra said it, I believe it, that settles it.)
Factor:
So:
(and we have one of our 4 roots)
or
Factor the difference of two cubes:
So
(and we have the second root)
or
Use the quadratic formula
(and that is the last two.)
Substituting back into the original equations, we derive the following solution set:
John
My calculator said it, I believe it, that settles it
