Question

用配方法解3x(x-1)=2(x-1)

为什么我算的总是无解。。不要用因式分解法。。配方法！~

Answer 1

3x(x-1)=2(x-1)
3x^2-3x=2x-2
3x^2-5x=-2
3(x^2-5x/3+25/36)-25/12=-2
3(x-5/6)^2=1/12
(x-5/6)^2=1/36
x-5/6=±1/6
当x-5/6=1/6时解得x=1
当x-5/6=-1/6时解得x=2/3

Answer 2

3x²-3x=2x-2
3x²-5x=-2
x²-5x/3=-2/3
x²-5x/3+25/36=-2/3+25/36
(x-5/6)²=1/36=(±1/6)²
x-5/6=±1/6
x=2/3,x=1

Answer 3

3x(x-1)=2(x-1)
3x²-3x=2x-2
3x²-5x+2=0
3(x-5/6）²-1/12=0
（x-5/6）²=1/36
（x-5/6）=±1/6
所以x1=1。x2=2/3

Answer 4

用配方法解3x(x-1)=2(x-1)
3x²-3x=2x-2
3x²-5x+2=0
3[x²-5x/3+(5/6)²]-3(5/6)²+2=0
3[x-(5/6)]²-(1/12)=0
[x-(5/6)]²=1/36
x-5/6=±1/6
x=±(1/6)+(5/6)
x1=1, x2=2/3

Answer 5

3x^2-5x=-2
3(x-5/6)^2=-2+25/12=1/12

x1=1 x2=2/3