Đáp án:
a. (2x+1)(x-1)=0
1) 2x + 1 = 0 ⇔ x = -1/2
2) x - 1 = 0 ⇔ x = 1
Vậy S = {-1/2 ; 1}
b. (x+2/3)(x-1/2)=0
1) x + 2/3 = 0 ⇔ x = -2/3
2) x - 1/2 = 0 ⇔ x = 1/2
Vậy S = {-2/3 ; 1/2}
c. (3x-1)(2x-3)(2x-3)(x+5)=0
1) 3x - 1 = x = 1/3
2) 2x - 3 = 0 ⇔ x = 3/2
3) x + 5 = 0 ⇔ x = -5
Vậy S = {1/3 ; 3/2 ; -5}
d. (3x-15)=2x(x-5)
⇔ 3x - 15 = 2x² - 10x
⇔ 3x - 15 - 2x² - 10x = 0
⇔ 3(x - 5) - 2x(x - 5) = 0
⇔ (x - 5)(3 - 2x) = 0
1) x - 5 = 0 ⇔ x = 5
2) 3 - 2x = 0 ⇔ x = 3/2
Vậy S = {5 ; 3/2}
e. x² - x =0
⇔ x(x - 1) = 0
1) x = 0
2) x - 1 = 0 ⇔ x = 1
Vậy S = {0 ; 1}
f. x² - 2x =0
⇔ x(x - 2) = 0
1) x = 0
2) x - 2 = 0 ⇔ x = 2
Vậy S = {0 ; 2}
g. x² - 3x =0
⇔ x(x - 3) = 0
1) x = 0
2) x - 3 = 0 ⇔ x = 3
Vậy S = {0 ; 3}
h. (x+1)(x+4)=(2-x)(x+2)
⇔ x² + 5x + 4 = 4 - x²
⇔ 2x² + 5x = 0
⇔ x.(2x + 5) = 0
1) x = 0
2) 2x + 5 = 0 ⇔ x = -5/2
Vậy S = {0 ; -5/2}
i. x³ -x=0
⇔ x(x² - 1) = 0
⇔ x(x - 1)(x + 1) = 0
1) x = 0
2) x - 1 = 0 ⇔ x = 1
3) x + 1 = 0 ⇔ x = -1
Vậy S = {0 ; 1 ; -1}
k. 2x³-8x=0
⇔ 2x(x² - 4) = 0
⇔ 2x(x - 2)(x + 2) = 0
1) 2x = 0 ⇔ x = 0
2) x - 2 = 0 ⇔ x = 2
3) x + 2 = 0 ⇔ x = -2
Vậy S = {0 ; 2 ; -2}
l. x² - 3x + 2=0
⇔ x² - x - 2x + 2 = 0
⇔ x(x - 1) - 2(x - 1) = 0
⇔ (x - 1)(x - 2) = 0
1) x - 1 = 0 ⇔ x = 1
2) x - 2 = 0 ⇔ x = 2
Vậy S = {1 ; 2}
m. x² - 10x + 21 = 0
⇔ x² - 2x.5 + 5² - 4 = 0
⇔ (x - 5)² - 2² = 0
⇔ (x - 5 - 2)(x - 5 + 2) = 0
⇔ (x - 7)(x - 3) = 0
1) x - 7 = 0 ⇔ x = 7
2) x - 3 = 0 ⇔ x = 3
Vậy S = {7 ; 3}
