# Thread: Solve x^2 - 2x + 2 > 0

1. ## Solve x^2 - 2x + 2 > 0

Hi,

I do not know where to start when solving inequalities of this variety:

$\displaystyle {x}^{2} -2x + 2 > 0$

I have no trouble when these quadratic inequalities are factorizable, but with this one I have tried pushing the symbols round and round in circles and can't find a way to simplify it. I typed this into an equation solver, and found that it is true for all x. Still, I am at a loss to determine how to prove it.

2. the graph of this appears to be imaginary and does not go thru the x axis and there is no part of the graph below x axis and also since it is a parabola opening up its domain is all real numbers or all points between the graph and the x axis. use the quadratic formula to find imaginary. hope this help some.

3. Originally Posted by borophyll
Hi,

I do not know where to start when solving inequalities of this variety:

$\displaystyle {x}^{2} -2x + 2 > 0$

I have no trouble when these quadratic inequalities are factorizable, but with this one I have tried pushing the symbols round and round in circles and can't find a way to simplify it. I typed this into an equation solver, and found that it is true for all x. Still, I am at a loss to determine how to prove it.

$\displaystyle x^2-2x+2> 0 \iff x^2-2x+1+1 > 0 \iff (x-1)^2+1 > 0$
$\displaystyle x^2-2x+2> 0 \iff x^2-2x+1+1 > 0 \iff (x-1)^2+1 > 0$