Question 530118: Please help me solve:
Find all real solutions of the given equation:
(x^2 - x)^2 - 63(x^2-x) - 648 = 0 Found 2 solutions by stanbon, KMST:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Find all real solutions of the given equation:
(x^2 - x)^2 - 63(x^2-x) - 648 = 0
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Let w = x^2-x
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Your problem:
w^2 - 63w - 648 = 0
Factor:
(w+9)(w-72) = 0
w = -9 or w = 72
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Solve for "w":
If w = -9 you get:
x^2-x = -9
x^2-x+9 = 0
Use the quadratic formula to solve.
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If w = 72
x^2-x 72
x^2-x-72 = 0
Factor:
(x-9)(x+8) - 0
x = 9 or x = -8
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Cheers,
Stan H.
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You can put this solution on YOUR website! Check my arithmetic, because I'm error prone, and sometimes my + and - sihgn magically inerconvert.
I would start by doing a variable change by defining
Then the equation is really
The solutions are and
Then you would have , with two real solutions and
and also
that would lead you to two other complex solutions
(