Question

解一元二次方程！！！要详细过程

1.2x+1=4x²
2.(x+1)²=(x+1)+56
3.(2x-1)²=(x-5)²
4.3(x-5)²=2(x-5)

Answer 1

1.2x+1=4x²
4x²-2x=1
x²-x/2=1/4
x²-x/2+1/16=5/16
(x-1/4)²=5/16
x=1/4+√5/4 x=1/4-√5/4

2.(x+1)²=(x+1)+56
(x+1)²-(x+1)-56=0
(x+1-8)(x+1+7)=0
(x-7)(x+8)=0
x=7或x=-8
3.(2x-1)²=(x-5)²
2x-1=x-5 2x-1=-(x-5)
x=-4 x=2

4.3(x-5)²=2(x-5)
3(x-5)²-2(x-5)=0
(x-5)(3x-15-2)=0
(x-5)(3x-17)=0
x=5 x=17/3