Question

Jika : ( x-6 )( x-9 ) = 18
Maka : x₁ - x₂ = . . .
​

Answer 1

Jawab:

(x - 6)(x - 9) = 18      

x² - 6x - 9x + 54 = 18

x² - 15x + 36 = 0

x² - 3x - 12x + 36 = 0

x(x - 3) - 12(x - 3) = 0

(x - 12)(x - 3) = 0

x - 12 = 0

      x₁ = 12

x - 3 = 0

    x₂ = 3

x₁ - x₂ = 12 - 3 = 9

atau

x₁ = 3

x₂ = 12

x₁ - x₂ = 3 - 12 = -9

Note:

untuk mencari akar dengan faktorisasi, persamaannya harus = 0, karena jika salah satu pengali kali 0 hasilnya 0:

(x - 12)(x - 3)

jika x = 12 maka: (12 - 12)(12 - 3) = 0 × 9 = 0 (benar)

itu alasan kenapa harus = 0

kalau  ( x-6 )( x-9 ) = 18, x - 6 = bukan 18 → x - 6 = 18 (salah)

18 × 15 = bukan 18

Answer 2

Merhaba Arkadaşlar

(x - 6) (x - 9) = 18

x² - 9x - 6x + 54 - 18 = 0

x² - 15x + 36 = 0

a = 1

b = -15

c = 36

x1 - x2 = √D/a

= √(b² - 4ac) ÷ a

= √((-15)² - 4 × 1 × 36) ÷ 1

= √(225 - 144)

= √81

= 9

Teşekkürler

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