SOLUTION: Quadratic Equations: Find real Solutions, show work. (2-y)^4=3(2-y)^2+1

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Question 1067958: Quadratic Equations: Find real Solutions, show work.
(2-y)^4=3(2-y)^2+1
Found 2 solutions by t0hierry, ikleyn:
Answer by t0hierry(194) About Me  (Show Source):
You can put this solution on YOUR website!
Change variable x = (2 -y)^2
The equation becomes
x^2 - 3x - 1 = 0
whose solutions are
x+=+3%2F2+%2B_+sqrt%2813%29%2F2
2+-+y+=+%2B_+sqrt%5B%283+%2B_+sqrt%2813%29%291%2F2%5D
y+=+2+%2B_+sqrt%5B%283+%2B_+sqrt%2813%29%291%2F2%5D

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
Introduce new variable x = (2 -y)^2

The equation becomes

x^2 - 3x - 1 = 0

whose solutions are 

x%5B1%2C2%5D = %283+%2B-+sqrt%2813%29%29%2F2.


Hence, 2+-+y = +/- sqrt%28%283+%2B-+sqrt%2813%29%29%2F2%29,


y = 2+%2B-+sqrt%28%283+%2B-+sqrt%2813%29%29%2F2%29.

Two of four roots with the sign "-" (minus) under the square radical are complex numbers.