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Posted by markr on 28/6/2009, 7:57 pm, in reply to "Anutter Li'l proof thing"
Need three unique, non-zero solutions to
x^2 + x - 7/x = N
Since x != 0,
x^3 + x^2 - Nx - 7 = 0
As we all know, given x^3 + Bx^2 + Cx + D = 0,
B is the opposite of the sum of the roots, and
D is the opposite of the product of the roots
In this case,
B = 1, so the sum of the roots is -1
D = -7, so the product of the roots is 7
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