CHI asked in 科學及數學數學 · 1 decade ago

我想問咩野係completing square????thxxx10分=]

同埋點計的呢????

2 Answers

Rating
  • 1 decade ago
    Favorite Answer

    要解 Completing Square,先要知道 Perfect Square

    Perfect Square:

    (a + b)² = a² + 2ab + b²

    方程:

    x² - 5x + 6 = 0

    (x² - 5x + ( 5 / 2(1) )² ) + 6 - ( 5 / 2(1) )² = 0

    (x - 5 / 2)² - 1 / 4 = 0

    x - 5 / 2 = ±1 / 2

    x = (5 ± 1) /2 = 3 or 2

    x² + 7x - 5 = 0

    (x² + 7x + ( 7 / 2(1) )² ) - 5 - ( 7 / 2(1) )² = 0

    (x + 7 / 2)² - 69 / 4 = 0

    x + 7 / 2 = ±√69 / 2

    x = (-7 ±√69) / 2

  • ?
    Lv 5
    1 decade ago

    Completing Square 即係將 有 2 次方既 方程式 「整」到 佢 變成 (X + ?)² 咁款!跟住求答案!

    e.g. Solve x² + 6x – 7 = 0 by completing the square

    x² + 6x = 7

    因為我地知道 x² + 6x + 9 = (x + 3)²

    所以我地「砌」個 "+ 9" 入去

    x² + 6x + 9 = 7 + 9

    (x + 3)² = 16

    (x + 3)² = 4²

    所以 (x + 3) = +4 或者 -4

    x + 3 = 4 或者 x + 3 = -4

    x = 1 或者 x = -7

    上述既方法就叫做 “Completing square ”

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