※ 引述《magiclass (課堂上玩數學)》之銘言：
: 三次多項式x^3+ax^2+bx+2=0的三根成等差，
: 且a,b皆為整數。
: 求a=? b=?
x(x - r)(x + r) = x(x^2 - r^2)
= x^3 - xr^2
(x - k)^3 - (x - k)r^2 = x^3 + ax^2 + bx + 2
= x^3 - 3kx^2 + x[3k^2 - r^2] - k^3 + kr^2
2 = kr^2 - k^3 = -k(k^2 - r^2)
a = -3k
b = 3k^2 - r^2
6 = a[b - (2 / 9) a^2]
=> 54 = a[9b - 2a^2]
滿足上是關係的(a, b)都是
a = 3, b = 4 公差為i!
a = 6, b = 9
a = -3, b = 0
a = -6, b = 7
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