※ 引述《adamchi (adamchi)》之銘言：
: 證明方程式
: X^3-3X^2-2^(1/2)X-1= 0 存在唯一一個正根
Let f(x) = x^3 - 3x^2 - sqrt(2)x - 1
f'(x) = 3x^2 - 6x - sqrt(2)
f"(x) = 6x - 6
f(x) has local maximum at x = 1-sqrt(1+sqrt(2)/3),
and f(1-sqrt(1+sqrt(2)/3)) < 0;
f(x) has local minimum at x = 1+sqrt(1+sqrt(2)/3),
and f(1+sqrt(1+sqrt(2)/3)) < 0.
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