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Math Help - Solve x^2 - 2x + 2 > 0

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

    Hi,

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

    {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.

    Thanks in advance
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  2. #2
    Super Member bigwave's Avatar
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    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.
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  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by borophyll View Post
    Hi,

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

    {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.

    Thanks in advance
    Complete the square. This gives

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

    Since squares are always bigger than zero the inequality is always true.
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  4. #4
    Junior Member
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    Quote Originally Posted by TheEmptySet View Post
    Complete the square. This gives

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

    Since squares are always bigger than zero the inequality is always true.
    Fantastic! I knew it would be something simple, thanks.
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