数学之美团为你解答
因为(√2 +³√3)² = 2 + 2√2*³√3 + (³√3)²
可得方程
(x² - 2)³ = [ (√2 +³√3)² - 2 ]³
整理得 x⁶ - 6x⁴ +12x² - 8 = 0
即 f(x) = x⁶ - 6x⁴ +12x² - 8x = √2 +³√3(x - √2)³ = 3x³ - 3√2 x² + 6x - 2√2 = 3x³+6x - 3 = 3√2 x² + 2√2(x³ +6x - 3)² = 2(3x² + 2)²x⁶ - 6x⁴ - 6x³ + 12x² - 36x + 1 = 0