Senin, 10 September 2018

Persamaan Kuadrat (Jawaban Soal Latihan 1) bagian 2

  1. Selesaikan persamaan kuadrat berikut :
    1. 5x2 – 10x = 0
    2. 2(x - 2)2 = 8
    3. 15x2 + 16x + 4 = 0
    4. x2-2x3-1=0
  2. Selesaikan persamaan kuadrat berikut dengan cara yang paling tepat dan cepat :
    1. (x - 1)(x - 2) = 12
    2. (x + 1)(3x - 2) = 1 + x
    3. x+2x=3+2xx
    4. x-62=-4x
    5. x+2=x-4
    6. x-3x+3+x+3x-3=3
    7. x+1x+2+x+2x+1=212
    8. x+2+x+2-6=0
    9. x4 - 13x2 + 36 = 0
    10. (x2 + 1)2 - 3(x2 + 1) + 2 = 0
Jawab :
    1. 5x2 – 10x = 0
      5x (x - 2) = 0
      5x = 0 atau x - 2 = 0
      x = 0 atau x = 2
    2. 2 (x - 2)2 = 8
      (x - 2)2 = 82
      (x - 2)2 = 4
      x - 2 = 4
      x - 2 = ± 2
      x = 2 ± 2
      x = 2 + 2 atau x = 2 - 2
      x = 4 atau x = 0
    3. 15x2 + 16 x + 4 = 0
      (3x + 2)(5x + 2) = 0
      3x + 2 = 0 atau 5x + 2 = 0
      3x = -2 atau 5x = -2
      x = -23 atau x = -25
    4. x2-2x3-1=0

      x2-23x-1=0

      x2-23x=1

      x-32=1+3

      x-32=4

      x-3=4

      x-3=±2

      x=3±2

      x=3+2 atau x=3-2
    1. (x-1)(x-2) = 12
      x2 - 2x - x + 2 = 12
      x2 - 3x + 2 -12 = 0
      x2 - 3x - 10 = 0
      (x-5)(x+2) = 0
      x - 5 = 0 atau x + 2 = 0
      x = 5              x = -2
    2. (x+1)(3x-2) = 1 + x
      3x2 - 2x + 3x - 2 = 1 + x
      3x2 + x - 2 = 1 + x
      3x2 + x - x - 2 - 1 = 0
      3x2 - 3 = 0
      3x2 = 3
      x2=33
      x2 = 1
      x=1
      x = ± 1
      x = -1 atau x = 1
    3. x+2x=3+2xx
      x2 + 2 = 3 + 2x
      x2 - 2x + 2 - 3 = 0
      x2 - 2x - 1 = 0
      x2 - 2x = 1
      (x - 1)2 = 1 + 1
      (x - 1)2 = 2
      x - 1 = 2
      x - 1 = ±2
      x = 1 ± 2
      x = 1 + 2 atau x = 1 - 2
    4. x-62=-4x
      x2-62=-4x
      12x2-3x=-4
      12x2-3x+4=0
      x2 - 6x + 8 = 0
      (x - 4)(x - 2) = 0
      x - 4 = 0 atau x - 2 = 0
      x = 4 atau x = 2
    5. x+2=x-4
      x + 2 = (x - 4)2
      x + 2 = (x - 4)(x - 4)
      x + 2 = x2 - 4x - 4x + 16
      x + 2 = x2 - 8x + 16
      x2 - 8x - x + 16 - 2 = 0
      x2 - 9x + 14 = 0
      (x - 7)(x - 2) = 0
      x - 7 = 0 atau x - 2 = 0
      x = 7 atau x = 2
    6. x-3x+3+x+3x-3=3
      x-3x+3 x-3x-3 +x+3x-3 x+3x+3=3
      x2-3x-3x+3x2-3x+3x-3+x2+3x+3x+3x2-3x+3x-3=3
      x2-23x+3x2-3+x2+23x+3x2-3=3
      x2+x2-23x+23x+3+3x2-3=3
      2x2+6x2-3=3
      2x2 + 6 = 3 ( x2 - 3 )
      2x2 + 6 = 3x2 - 9
      3x2 - 2x2 - 9 - 6 = 0
      x2 - 15 = 0
      x2 = 15
      x = 15
      x = ±15
      x = 15 atau x = -15
    7. x+1x+2+x+2x+1=212
      (x + 1)(x + 1)(x + 2)(x + 1)+(x + 2)(x + 2)(x + 1)(x + 2)=52
      x2+2x+1x2+3x+2+x2+4x+4x2+3x+2=52
      x2+x2+2x+4x+1+4x2+3x+2=52
      2x2+6x+5x2+3x+2=52
      2x2+6x+5=52x2+3x+2
      4x2+12x+10=5x2+15x+10
      5x2-4x2+15x-12x+10-10=0
      x2 + 3x = 0
      x(x + 3) = 0
      x = 0 atau x + 3 = 0
                      x = 3
    8. x+2+x+2-6=0
      x+2-6+x+2=0
      x-4+x+2=0
      x+2=-x+4
      x + 2 = (-x + 4)2
      x + 2 = (-x + 4)(-x + 4)
      x + 2 = x2 - 4x - 4x + 16
      x + 2 = x2 - 8x + 16
      x2 - 8x - x + 16 - 2 = 0
      x2 - 9x + 14 = 0
      (x - 7)(x - 2) = 0
      x - 7 = 0 atau x - 2 = 0
      x = 7 atau x = 2
    9. x4 - 13x2 + 36 = 0
      (x2 - 4)(x2 - 9) = 0
      x2 - 4 = 0 atau x2 - 9 = 0
      x2 = 4 atau x2 = 9
      x = 4 atau x = 9
      x = ±2 atau x = ±3
      x = 2 atau x = -2 atau x = 3 atau x = -3
    10. (x2 + 1)2 - 3(x2 + 1) + 2 = 0
      misal : a = x2 + 1
      a2 - 3a + 2 = 0
      (a - 2)(a - 1) = 0
      a - 2 = 0 atau a - 1 = 0
      a = 2 atau a = 1
      x2 + 1 = 2 atau x2 + 1 = 1
      x2 = 2 - 1 atau x2 = 1 - 1
      x2 = 1 atau x2 = 0
      x = 1 atau x = 0
      x = ±1 atau x = 0
      x = 1 atau x = -1 atau x = 0

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