f4 math (1題5分)

x4 + 6x³ - 7x² - 36x + 6 = 0

(x4 - 7x² + 6) + (6x³ - 36x) = 0

[(x²)² - 7(x²) + 6] + 6x(x² - 6) = 0

(x²-6)(x²-1) + 6x(x²-6) = 0

(x²-6)[(x²-1) + 6x] = 0

(x²-6)(x² + 6x - 1) = 0

[x² - (√6)²](x² + 6x - 1) = 0

(x-√6)(x+√6)(x² + 6x - 1) = 0 ............... by the identity a²-b² = (a+b)(a-b)

x-√6 = 0 or x+√6 = 0 or x² + 6x - 1 = 0

x = √6 or x = -√6 or x² + 6x - 1 = 0 .......... (1)

Considering x² + 6x - 1 = 0

x = [-6±√(6²-4(1)(-1))]/2(1)
x = [-6±√(36 + 4)]/2
x = [-6±√40]/2
x = [-6±2√10]/2
x = -3±√10
x = -3+√10 or x = -3-√10 ............ (2)

Combining (1) and (2),
x = √6 or x = -√6 or x = -3+√10 or x = -3-√10







2006-12-10 20:20:22 補充：
小小補充：factorizaton (因式分解) 常用到的恆等式有a²-b² = (a-b)(a+b) ..... 最常用(a-b)² = a²-2ab+b²(a+b)² = a²+2ab+b²另外：ax²+bx+c = 0 公式是 x = [-b±√(b²-4ac)]/2a