解方程
版主: thepiano
Re: 解方程
95 斗南高中考過，出題者改數字，結果被您捉到 bug
f(t) = (t - 1)(t - 8)(t - 27)(t - 64) - x^2(t - 8)(t - 27)(t - 64) - y^2(t - 1)(t - 27)(t - 64) - z^2(t - 1)(t - 8)(t - 64) - w^2(t - 1)(t - 8)(t - 27)
易知 f(25) = f(36) = f(49) = f(64) = 0
由根與係數可知 25 + 36 + 49 + 64 = 1 + 8 + 27 + 64 + x^2 + y^2 + z^2 + w^2
x^2 + y^2 + z^2 + w^2 = 74
f(t) = (t - 1)(t - 8)(t - 27)(t - 64) - x^2(t - 8)(t - 27)(t - 64) - y^2(t - 1)(t - 27)(t - 64) - z^2(t - 1)(t - 8)(t - 64) - w^2(t - 1)(t - 8)(t - 27)
易知 f(25) = f(36) = f(49) = f(64) = 0
由根與係數可知 25 + 36 + 49 + 64 = 1 + 8 + 27 + 64 + x^2 + y^2 + z^2 + w^2
x^2 + y^2 + z^2 + w^2 = 74