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maths

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if x=1/(2-3^1/2)
prove that
x^3-2x^2-7x+5=3

  • maths - ,

    start with the equation:
    x^3 - 2x^2 - 7x + 2 = 0
    after two tries, I found x = -2 to be a solution
    so it factors to
    (x+2)(x^2-4x+1) = 0
    from the second ...
    x = (4 ± √12)/2 = 2 ± √3

    but you told me x = 1/(2-√3)
    rationalizing this ...
    1/(2-√3) * (2+√3)/(2+√3)
    = (2+√3)/(4 - 3) = 2 + √3

    which is one of the values for x I got by solving the equation.

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