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
Algebra.Com
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): You can put this solution on YOUR website!
Not exactly trivial. There is more to it than meets the eye at first glance.
Substitute the first into the second:
^2)
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:
\ =\ 0)
So:
(and we have one of our 4 roots)
or
Factor the difference of two cubes:
(x^2\ +\ x\ +\ 1)\ =\ 0)
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:
,\,\left(1,1\right),\,\left(\frac{-1\ +\ i\sqrt{3}}{2}\,,\,\frac{-1\ -\ i\sqrt{3}}{2}\right),\,\left(\frac{-1\ -\ i\sqrt{3}}{2}\,,\,\frac{-1\ +\ i\sqrt{3}}{2}\right)\right})
John
My calculator said it, I believe it, that settles it
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