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Math Help - Find the equation

  1. #1
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    Exclamation Find the equation

    Find the equation of the line that passes trough point (0,1) such that the area, S, of the region enclosed by this line and the parabola y=x^2 is (5√5)/6.

    This is what I did:
    I found the equation of the line which is y=x+1
    Then, I put x^2=x+1
    x^2-x-1=0
    α+β=-1
    αβ=-1
    S=integral of (x+1-x^2)dx [α,β].
    It gave me (5√5)/6.
    I don't know how to continue to find out the equation.
    Please help me!
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  2. #2
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    Re: Find the equation

    How did you manage to get y = x + 1? There are an INFINITE number of lines that this could possibly be. It should be y = mx + 1.
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  3. #3
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    Re: Find the equation

    This is what I did:
    I found the equation of the line which is y=mx+1
    Then, I put x^2=mx+1
    x^2-mx-1=0
    α+β=m
    αβ=-1
    S=integral of (mx+1-x^2)dx [α,β].
    It gave me 1/6(m+2)^3
    I put 1/6(m+2)^3=(5√5)/6
    It gave me that m=-2cubic root of 5√5
    So, the equation is y=(=-2cubic root of 5√5)x+1

    I know that my answer is wrong... because it cannot give a number like this.. but I cannot find out where is my mistake.
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  4. #4
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    Re: Find the equation

    Find the equation-area-problem.png
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  5. #5
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    Re: Find the equation

    Find the equation-area-problem-2.pngPlease have the complete solution
    Thanks from hahalol
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