因式分解x的四次-12x的二次+4?
回答 (3)
2016-09-14 9:11 am
✔ 最佳答案
令 x⁴- 12x² + 4 = (x² - a)² - (bx)² = x⁴- (2a+b²)x² + a² ,比較係數得 2a+b² = 12 , a² = 4。
若 a = 2 , 則 b² = 8 不合 ,
若 a = - 2 , 則 b² = 16 , b = ±4 得 x⁴- 12x² + 4 = (x² + 2)² - (4x)² = (x² - 4x + 2) (x² + 4x + 2)。
2016-09-14 8:57 am
x⁴ - 12x² + 4
= (x²)² -12x² + 4
設 y = x²
x⁴ - 12x² + 4
= y² -12y + 4
= y² -12y + 6² - 6² + 4
= (y-6)² - 32
= (y-6)² - (√32)²
= (y- 6 + √32) (y-6 -√32)
= (y- 6 + 4√2) (y-6 -4√2)
= (x²- 6 + 4√2) (x²-6 -4√2)
= (x²)² -12x² + 4
設 y = x²
x⁴ - 12x² + 4
= y² -12y + 4
= y² -12y + 6² - 6² + 4
= (y-6)² - 32
= (y-6)² - (√32)²
= (y- 6 + √32) (y-6 -√32)
= (y- 6 + 4√2) (y-6 -4√2)
= (x²- 6 + 4√2) (x²-6 -4√2)
2016-10-14 1:08 am
x^4-12x^2+4
=(x^2+2+2x)(x^2+2-2x)
=(x^2+2+2x)(x^2+2-2x)
收錄日期: 2021-04-18 15:37:05
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https://hk.answers.yahoo.com/question/index?qid=20160914002202AAidoMQ