SOLUTION: Solve (x^2-x)^2+(x^2-x)-2=0 in exact values

Question 990252: Solve
(x^2-x)^2+(x^2-x)-2=0 in exact values
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Your equation is

= .

The standard and universal method for solving such equations is introducing new variable.

In our case let y = .

Then the original equation takes the form

= .

It is a quadratic equation. You can easily solve it by applying the quadratic formula or the Viete's theorem. Its roots are

= -2,    = 1.

Now we should solve two quadratic equations to find x. They are

=         (1)

and

= .         (2)

The first of these two equations is

= .

It has no real solutions (the discriminant d = = 1 - 4*2 = -7 is negative).

The second of these two equations is

= .

It has two roots    = .

Answer. The given equation has two roots: and .

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Solve
(x^2-x)^2+(x^2-x)-2=0 in exact values

Exact values:
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