# xy+3x-2y-6以及x的4平方+3x的平方+4,最後設a+b=8,ab=3 a平方加b平方 a3次方加b的三次方 a-b?

### 2 個解答

• 5 年前
最佳解答

1. xy + 3x - 2y - 6

= x(y + 3) - 2(y + 3)

= (x - 2)(y + 3)

2. x⁴＋3x²＋4

＝x⁴＋4x²＋4－x²

= (x²＋2)²－x²

= (x²＋x＋2)(x²－x＋2)

3. a² + b²

= (a² + 2ab + b²) - 2ab

= (a + b)² - 2ab

= 8² - 2 × 3

= 58

a³ + b³

= (a + b)(a² - ab + b²)

= (a + b)[(a² + b²) - ab]

= 8 × (58 - 3)

= 440

若 a＞b，則 a－b

= √(a－b)²

= √(a²＋b²－2ab)

= √(58－2 × 3]

= √52

= 2√13

若 a＜b，則 a－b＝-2√13

• 5 年前

1.

xy + 3x - 2y - 6

= (xy + 3x) - (2y + 6)

= x(y + 3) - 2(y + 3)

= (x - 2)(y + 3) ...... [答案]

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2.

x⁴ + 3x² + 4 不可因式分解

若為 x⁴ + 3x² - 4，則：

x⁴ + 3x² - 4

= (x²)² + 3(x²) - 4

= (x² + 1)(x² - 4)

= (x² + 1)(x² - 2²)

= (x² + 1)(x + 2)(x - 2) ...... [答案]

====

3.

a² + b²

= (a² + 2ab + b²) - 2ab

= (a + b)² - 2ab

= 8² - 2 × 3

= 58 ...... [答案]

a³ + b³

= (a + b)(a² - ab + b²)

= (a + b)[(a² + b²) - ab]

= (a + b)[(a² + 2ab + b²) - 3ab]

= (a + b)[(a + b)² - 3ab]

= 8 × [8² - 3 × 3]

= 8 × 55

= 440 ...... [答案]

a - b

= ±√(a - b)²

= ±√[(a + b)² - 4ab]

= ±√[8² - 4 × 3]

= ±√52

= ±2√13 ...... [答案]