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Math Help - Unique resolution

  1. #1
    Super Member dhiab's Avatar
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    Unique resolution

    Prove that equation , accepts an unique resolution : and :
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by dhiab View Post
    Prove that equation , accepts an unique resolution : and :
    put g(x)=f(x)-x, then:

    g'(x)=(-2x^2+x+3)e^{-x}-1

    Now look at -2x^2+x+3 this has roots at x=-1 and 3/2, so -2x^2+x+3 has constant sign for x>3/2, a quick check shows that this is negative. Hence g'(x)<0 for x>3/2

    Thus g(x) is decreasing when x>3/2. To complete the proof it remains to show that g(3/2) is positive and g(2) is negative.

    CB
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  3. #3
    Super Member dhiab's Avatar
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    Hello captain thank you for your resolution Ajout : alpha = 1.91 and g(1.5)=0.5 , g(2)=-0.12
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