流佑 發問時間: 科學數學 · 5 年前

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

評分
  • 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]

    ====

    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]

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