Question 520627: write the solutions of the inequality
x^2-6x+9
Answer by tinbar(133)   (Show Source):
You can put this solution on YOUR website! First find where it's equal to 0. These points will determine the bounds of the set of numbers we want to satisfy the question.
x^2-6x+9=0 can be factored and is thus equivalent to (x-3)^2=0
So when x = 3, the function goes to 0. Let's pick a number greater than 3, and one lower than 3 and see what happens to the given function.
For x = 4; (x-3)^2 = (4-3)^2 = 1, which is greater than 0. In fact if x>3, then (x-3)>1, which means for all x>3, (x-3)^2 > 0. So no x>3 will be part of our solution.
For x = 2; (x-3) < 0, however, (x-3)^2 > 0, since any number squared becomes positive. So it turns out for x<3, (x-3)^2 > 0 as well.
So ultimately, the only solution is x=3, since at x = 3, x^2-6x+9=0. For all other x, x^2-6x+9>0.
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