SOLUTION: (2x-2)^2>=(3x-2)(x-3)

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Question 802317: (2x-2)^2>=(3x-2)(x-3)
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
(1)%282x-2%29%5E2%3E=%283x-2%29%2A%28x-3%29 or
(2)%282x-2%29%5E2-%283x-2%29%2A%28x-3%29%3E=0
Now expand all parenthesis in (2) to get
(3)%284x%5E2-8x%2B4%29-%283x%5E2-2x-9x%2B6%29%3E=0 or
(4)x%5E2%2B3x-2%3E=0
The parabola of (4) opens upward but goes negative between the limits
(5)%28-3-sqrt%2817%29%29%2F2%3C=x%3C=%28-3%2Bsqrt%2817%29%29%2F2
Since the solution domain is for f(x) to greater or equal to zero the answer is
(6)x%3C=%28-3-sqrt%2817%29%29%2F2 and x%3E=%28-3%2Bsqrt%2817%29%29%2F2