5) (1 –x )(5x+3) = (3x -7)(x-1)
⇔ 5x +3 -5x² -3x = 3x² -3x -7x +7
⇔ 5x -5x² -3x -3x² +7x +3x = -3 +7
⇔ 12x -8x² = 4
⇔ -8x² +12x -4 = 0
⇔ -8x² +8x +4x -4 = 0
⇔ -8x.(x -1) +4.(x -1) = 0
⇔ (x-1).(-8x +4) = 0
TH1: x-1 = 0 ⇒ x =1
TH2: -8x +4 = 0 ⇒ -8x = -4 ⇒ x = 1/2
Vậy S= {1; 1/2}
7) (2x - 7)² – 6(2x - 7)(x - 3) = 0
⇔ (2x -7).[(2x-7)-6.(x-3)] = 0
⇔ (2x -7).(2x -7 -6x +18) = 0
⇔ (2x -7).(-4x +11) =0
TH1: 2x -7 = 0
⇔ 2x = 7
⇔ x = 7/2
TH2: -4x +11 =0
⇔ -4x = -11
⇔ x = 11/4
Vậy S= {7/2; 11/4}
6) 2x(2x-3) = (3 – 2x)(2-5x)
⇔ 2x(2x -3) = (3-2x).(2 -5x)
⇔ 2x(2x -3) +(2x -3).(2 -5x) = 0
⇔ (2x -3).(2x +2-5x) = 0
⇔ (2x -3).(2 -3x) = 0
TH1: 2x -3 = 0
⇔ 2x = 3
⇔ x = 3/2
TH2: 2 -3x = 0
⇔ -3x = -2
⇔ x = 2/3
Vậy S= { 3/2; 2/3 }
8) (x-2)(x+1) = x² -4
⇔ (x-2)(x+1) -(x² -4) = 0
⇔ (x-2)(x+1) -(x-2).(x+2) = 0
⇔ (x-2).(x+1 -x -2) = 0
⇔ (x-2).(-1) = 0
⇔ x-2 = 0 ⇔ x = 2
Vậy S= {2}
9) x² – 5x + 6 = 0
⇔ x² -2x -3x +6 = 0
⇔ x(x-2) -3(x-2) = 0
⇔ (x-2).(x-3) = 0
TH1: x-2 = 0 ⇔ x= 2
TH2: x-3 = 0 ⇔ x= 3
Vậy S= { 2; 3 }
10) 2x³ + 6x² = x² + 3x
⇔ 2x³ +6x² -x² -3x = 0
⇔ 2x²(x+3) -x(x+3) = 0
⇔ (x+3).(2x² -x) = 0
TH1: x+3 = 0 ⇔ x= -3
TH2: 2x² -x = 0
⇔ x(2x-1) = 0
⇔ x= 0 hoặc 2x -1 = 0 ⇒ x = 1/2
Vậy S= { 0; -3; 1/2 }
11) (2x + 5)² = (x + 2)²
⇔ 4x² +20x +25 = x² +4x +4
⇔ 4x² +20x +25 - x² -4x -4 = 0
⇔ 3x² +16x +21 = 0
⇔ 3x² +7x +9x +21 = 0
⇔ x(3x +7) +3(3x +7) = 0
⇔ (3x +7).(x +3) = 0
TH1: 3x +7 = 0 ⇒ x = -7/3
TH2: x +3 = 0 ⇒ x = -3
Vậy S= { -7/3; -3 }
