Question

九年级一元二次方程

2X的平方-5X-1=0
3分之一的X的平方-X-2=0
3分之2的X平方-X-1=0 用配方法做

Answer 1

2X的平方-5X-1=0
2(x²-5x/2-1/2)=0
2[(x-5/4)²-1/2-25/16]=0
2[(x-5/4)²-(√33/4)²]=0
2(x-5/4+√33/4)(x-5/4-√33/4)=0
解得x=5/4-√33/4或x=5/4+√33/4
3分之一的X的平方-X-2=0
x²-3x-6=0
(x-3/2)²-9/4-6=0
(x-3/2)²-(√33/2)²=0
(x-3/2-√33/2)(x-3/2+√33/2)=0
解得x=3/2+√33/2或x=3/2-√33/2
3分之2的X平方-X-1=0
2x²-3x-3=0
2(x²-3x/2-3/2)=0
2[(x-3/4)²-9/16-3/2]=0
2[(x-3/4)²-(√33/4)²]=0
2(x-3/4-√33/4)(x-3/4+√33/4)=0
解得x=3/4+√33/4或x=3/4-√33/4
希望能帮到你，祝学习进步O(∩_∩)O

Answer 2

2X²-5X-1=0
2(x²-5/2x)-1=0
2(x-5/4)²-33/8=0
(x-5/4)²=33/16
x-5/4=±√33/4
x=(5+√33)/4,x=(5-√33)/4

x²/3-X-2=0
x²-3x-6=0
(x-3/2)²-33/4=0
(x-3/2)²=33/4
x-3/2=±√33/2
x=(3+√33)/2,x=(3-√33)/2

2x²/3-X-1=0
2x²-3x-3=0
x²-3/2x-3/2=0
(x-3/4)²-33/16=0
(x-3/4)²=33/16
x-3/4=±√33/4
x=(3+√33)/4,x=(3-√33)/4

追问

最后两道题目 你抄错了是
3分之1 X的平方-X-2=0
3分之2 X的平方-X-1=0

追答

3分之1 X的平方-X-2=0
是1/3(x²-x-2)=0吗？
1/3(x²-x-2)=0
x²-x-2=0
(x-1/2)²-9/4=0
x-1/2=±3/2
x=(1-3)/2=-1,x=(1+3)/2=2

3分之2 X的平方-X-1=0
x²-x-1=0
(x-1/2)²-5/4=0
x-1/2=±√5/2
x=(1+√5)/2,x=(1-√5)/2

Answer 3

3分之2的X平方-X-1=0
x^2-3/2x-3/2=0
x^2-3/2x+9/16-9/16-3/2=0
(x-3/4)^2=33/16 , x=(3±√33)/4
1、2用求根公式