x^3 - 3x + 1 = 0

x^3 - 3x + 1 = 0

x^3 - x - 2x +1 = 0
x(x^2 - 1) - 2x + 1 = 0
x(x + 1)(x-1) - 2x + 2 - 1 = 0
x(x + 1)(x - 1) - 2(x-1) = 1
(x-1)( x^2 + x -2) = 1

？？？？

x^3  = 3x - 1

CubicEquation20251114.java

=== 二分法求解（近似解，精度1e-8）===
验证 x = -1.87938524: 左边=-6.63815571, 右边=-6.63815572, 误差=9.08377640e-09
验证 x = 0.34729636: 左边=0.04188907, 右边=0.04188907, 误差=4.80404330e-09
验证 x = 1.53208889: 左边=3.59626666, 右边=3.59626666, 误差=2.86361246e-09

=== 卡尔达诺公式求解（精确解）===
验证 x = -3.25519073: 左边=-34.49286895, 右边=-10.76557218, 误差=2.37272968e+01
验证 x = 2.65365579: 左边=18.68674971, 右边=6.96096738, 误差=1.17257823e+01
验证 x = 0.60153493: 左边=0.21766197, 右边=0.80460480, 误差=5.86942826e-01