1. B ( x^2 + 3x - 6 = 0 )
Penyelesaian =
LOGIKA AJA
2. A ( 4x^2 +4x - 5 = 0 )
Penyelesaian =
(2x + 1)² = (2x + 1) × (2x + 1)
(ax + b) × (ax + b) = (ax × ax) + (ax × b) + (b × ax) + (b ×b)
(2x + 1) × (2x + 1) = (2x ×2x) + (2x × 1) + (1 × 2x) + (1 × 1)
(2x + 1)² = 4x² + 2x + 2x + 1
(2x + 1)² = 4x² + 4x + 1
Jadi, (2x + 1)² = 4x² + 4x + 1
Maka,
4x² + 4x - 5 = 0
(2x + 1)² = 6
4x² + 4x + 1 = 6
Untuk memindahkan 6, kita kurangi 6 di kedua sisi
4x² + 4x + 1 - 6 = 6 - 6
4x² + 4x - 5 = 0
3. C ( X = 7 atau X = -2 )
Penyelesaian =
(2x-5)²-81 = 0
(2x)²-2.2x.(-5)+(-5)²-81 = 0
4x²-20x+25-81 = 0
4x²-20x-56 = 0
(2x)²-2.2x.(-5)+(-5)²-81 = 0
4x²-20x+25-81 = 0
4x²-20x-56 = 0
kdua ruas dibagi 4, menjadi :
x²-5x-14 = 0
(x+2).(x-7) = 0
x+2 = 0
x = -2
atau
x-7 = 0
x = 7
4. B ( X1 = 8 dan X2 = -3 )
Penyelesaian
x + 8/x = ( 4x - 5 / 3 )
3 ( x + 8/x ) = 4x - 5
3x + 24/x = 4x - 5
24/x = 4x - 5 - 3x
24/x = x - 5
24 = ( x- 5 ) x
24 = x^2 - 5x
0 = x^2 - 5x - 24
( x - 8 ) ( x + 3 )
x = 8 // x = - 3
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