SOLUTION: Solve the following system of nonlinear equations? y=x^4-2x^3-17x^2+4 y=-3x^4-2x^3+20x^2-5

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Question 328149: Solve the following system of nonlinear equations?
y=x^4-2x^3-17x^2+4
y=-3x^4-2x^3+20x^2-5
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4-2x%5E3-17x%5E2%2B4=-3x%5E4-2x%5E3%2B20x%5E2-5
4x%5E4-37x%5E2%2B9=0
Use a substitution.
Let u=x%5E2, u%5E2=x%5E4
4u%5E2-37u%2B9=0
%284u-1%29%28u-9%29=0
Two solutions in u:
+4u-1=0
+4u=1
+u=1%2F4
+x%5E2=1%2F4
+highlight_green%28x=0+%2B-+1%2F2%29
.
.
.
u-9=0
u=9
x%5E2=9
highlight_green%28x=0+%2B-+3%29
Solve for y with each x using either equation.
highlight%28+x=1%2F2%29,y=%281%2F2%29%5E4-2%281%2F2%29%5E3-17%281%2F2%29%5E2%2B4=1%2F16-1%2F4-17%2F4%2B4=-7%2F16
highlight%28y=-7%2F16%29
.
.
.
highlight%28+x=-1%2F2%29,y=%281%2F2%29%5E4%2B2%281%2F2%29%5E3-17%281%2F2%29%5E2%2B4=1%2F16%2B1%2F4-17%2F4%2B4=1%2F16
highlight%28y=1%2F16%29
.
.
.
highlight%28+x=3%29,y=3%5E4-2%283%29%5E3-17%283%29%5E2%2B4=81-54-153%2B4=-122
highlight%28y=-122%29
.
.
.
highlight%28+x=-3%29,y=3%5E4%2B2%283%29%5E3-17%283%29%5E2%2B4=81%2B54-153%2B4=-14
highlight%28y=-14%29