Question

4(2x-1)²=9(x+4)² (2x-3)²-4(2x-3)=12 (2x-1)²+(x+

4(2x-1)²=9(x+4)²

(2x-3)²-4(2x-3)=12

(2x-1)²+(x+2)²=(3x-2)²-15

3x(x-2)=2(2-x)

任何方法都行，并且做出解释，感谢

Answer 1

4(2x-1)²=9(x+4)²
2(2x-1)=±3(x+4)
4x-2=±(3x+12)
x=14或-10/7

(2x-3)²-4(2x-3)=12
((2x-3)+2)((2x-3)-6)=0
(2x-1)(2x-9)=0
2x-1=0或2x-9=0
x=1/2或9/2

(2x-1)²+(x+2)²=(3x-2)²-15
4x²-4x+1+x²+4x+4=9x²-12x+4-15
0=4x²-12x-16
x²-3x-4=0
(x-4)(x+1)=0
x=4或-1

3x(x-2)=2(2-x)
x=2或3x=-2(等式两边同时约分)
即x=2或-2/3

Answer 2

(1)
4(2x-1)^2=9(x+4)^2

2(2x-1) =± 3(x+4)
x=14 or x=-10/7

(2)

(2x-3)^2-4(2x-3)=12
(2x-3)^2-4(2x-3)-12 =0
(2x-3-6)(2x-3+2)=0
(2x-9)(2x-1)=0
x=1/2 or 9/2

(3)
(2x-1)^2+(x+2)^2=(3x-2)^2-15

(4x^2-4x+1)+(x^2+4x+4)=(9x^2-12x+4)-15
4x^2-12x-16=0
x^2-3x-4=0
(x-4)(x+1)=0
x=4 or -1

(4)
3x(x-2)=2(2-x)

3x(x-2)+2(x-2)=0
(x-2) (3x+2)=0
x=2 or -2/3

Answer 3

(1) 整理得： (4x-2)^2 - (3x+12)^2 =0
即(7x+10)(x-14)=0, ∴ x=-10/7 或 14
(2) 整理的：(2x-3)^2 -4(2x-3) -12=0
即(2x-3-6)(2x-3+2)=0，∴x=9/2 或 1/2
(3)整理得：(2x-1)^2 + 15 = (3x-2)^2 -(x+2)^2=4x(2x-4)
即4x^2 -4x +16=8x^2 -16x
即x^2 -3x -4=0
即(x-4)(x+1)=0, ∴x=4或-1
(4) 观察可得，x=2满足方程；若x≠2，则化简为-3x = 2, ∴x=-2/3或x=2

Answer 4

4(2x-1)²=9(x+4)²

2(2x-1)=3(x+4) or 2(1-2x)=3(x+4)
4x-2=3x+12 or 2-4x=3x+4
x=14 or x=-2/7

(2x-3)²-4(2x-3)=12

(2x-3-6)(2x-3+2)=0
x=9/2 or x=1/2

(2x-1)²+(x+2)²=(3x-2)²-15

4x²-4x+1+x²+4x+4=9x²-12x+4-15
4x²-12x-16=0
x²-3x-4=0
(x-4)(x+1)=0

x=4 or x=-1

3x(x-2)=2(2-x)

3x²-6x=4-2x
3x²-4x-4=0
(x-2)(3x+2)=0
x=2 or x=-2/3

Answer 5

追答