初二 一元二次方程 用因式分解法解 (详细过程)
(1)(x+y)(x+y-3)+2=0(2)(x-2)²-3(x-2)+2=0(3)(x+5)²-6(x+5)+9=0(4)(x²+y...
(1)(x+y)(x+y-3)+2=0
(2)(x-2)²-3(x-2)+2=0
(3)(x+5)²-6(x+5)+9=0
(4)(x²+y²+1)(x²+y²-3)=-4
(5)x²-2xy+y²+(x-y)-6=0 展开
(2)(x-2)²-3(x-2)+2=0
(3)(x+5)²-6(x+5)+9=0
(4)(x²+y²+1)(x²+y²-3)=-4
(5)x²-2xy+y²+(x-y)-6=0 展开
11个回答
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(1)(x+y)(x+y-3)+2=0
(x+y)²-3(x+y)+2=0
(x+y-2)(x+y-1)=0
解得x+y=2或x+y=1
(2)(x-2)²-3(x-2)+2=0
[(x-2)-2][(x-2)-1]=0
(x-4)(x-3)=0
解得x=4或x=3
(3)(x+5)²-6(x+5)+9=0
[(x+5)-3]²=0
(x+2)²=0
解得x=-2
(4)(x²+y²+1)(x²+y²-3)=-4
(x²+y²)²-2(x²+y²)-3+4=0
(x²+y²)²-2(x²+y²)+1=0
(x²+y²-1)²=0
解得x²+y²=1
(5)x²-2xy+y²+(x-y)-6=0
(x-y)²+(x-y)-6=0
(x-y+3)(x-y-2)=0
解得x-y=-3或x-y=2
希望能帮到你O(∩_∩)O
(x+y)²-3(x+y)+2=0
(x+y-2)(x+y-1)=0
解得x+y=2或x+y=1
(2)(x-2)²-3(x-2)+2=0
[(x-2)-2][(x-2)-1]=0
(x-4)(x-3)=0
解得x=4或x=3
(3)(x+5)²-6(x+5)+9=0
[(x+5)-3]²=0
(x+2)²=0
解得x=-2
(4)(x²+y²+1)(x²+y²-3)=-4
(x²+y²)²-2(x²+y²)-3+4=0
(x²+y²)²-2(x²+y²)+1=0
(x²+y²-1)²=0
解得x²+y²=1
(5)x²-2xy+y²+(x-y)-6=0
(x-y)²+(x-y)-6=0
(x-y+3)(x-y-2)=0
解得x-y=-3或x-y=2
希望能帮到你O(∩_∩)O
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(1)(x+y)(x+y-3)+2=0 (x+y)[(x+y)-3]+2=(x+y)²-3(x+y)+2=0因式分解(x+y-1)(x+y-2)=0得
x+y=1或x+y=2
(2)(x-2)²-3(x-2)+2=0
因式分解(x-2-1)(x-2-2)=(x-3)(x-4)=0得x=3或x=4
(3)(x+5)²-6(x+5)+9=0
因式分解(x+5-3)(x+5-3)=(x+2)²=0得x=-2
(4)(x²+y²+1)(x²+y²-3)=-4
得(x²+y²)²-2(x²+y²)+1=0分解因式(x²+y²-1)²=0得x²+y²=1
5)x²-2xy+y²+(x-y)-6=0得(x-y)²+(x-y)-6=0分解因式(x-y+3)(x-y-2)=0得x-y=-3或x-y=2
x+y=1或x+y=2
(2)(x-2)²-3(x-2)+2=0
因式分解(x-2-1)(x-2-2)=(x-3)(x-4)=0得x=3或x=4
(3)(x+5)²-6(x+5)+9=0
因式分解(x+5-3)(x+5-3)=(x+2)²=0得x=-2
(4)(x²+y²+1)(x²+y²-3)=-4
得(x²+y²)²-2(x²+y²)+1=0分解因式(x²+y²-1)²=0得x²+y²=1
5)x²-2xy+y²+(x-y)-6=0得(x-y)²+(x-y)-6=0分解因式(x-y+3)(x-y-2)=0得x-y=-3或x-y=2
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(1)(x+y)(x+y-3)+2=0
(x+y)²-3(x+y)+2=0
(x+y-2)(x+y-1)=0
x+y=2
x+y=1
∴此方程无解
(2)(x-2)²-3(x-2)+2=0
(x-2-2)(x-2-1)=0
(x-4)(x-3)=0
x-4=0 x-3=0
∴x=4 或 x=3
(3)(x+5)²-6(x+5)+9=0
(x+5-3)²=0
(x+2)²=0
∴x=-2
(4)(x²+y²+1)(x²+y²-3)=-4
(x²+y²)²-2(x²+y²)-3+4=0
(x²+y²)²-2(x²+y²)+1=0
(x²+y²+1)²=0
x²+y²+1=0
x²+y²=-1
∴此方程无解。
(5)x²-2xy+y²+(x-y)-6=0
(x-y)²+(x-y)-6=0
(x-y+3)(x-y-2)=0
x-y=-3 x-y=2
∴此方程无解。
你的题目有没有问题???
(x+y)²-3(x+y)+2=0
(x+y-2)(x+y-1)=0
x+y=2
x+y=1
∴此方程无解
(2)(x-2)²-3(x-2)+2=0
(x-2-2)(x-2-1)=0
(x-4)(x-3)=0
x-4=0 x-3=0
∴x=4 或 x=3
(3)(x+5)²-6(x+5)+9=0
(x+5-3)²=0
(x+2)²=0
∴x=-2
(4)(x²+y²+1)(x²+y²-3)=-4
(x²+y²)²-2(x²+y²)-3+4=0
(x²+y²)²-2(x²+y²)+1=0
(x²+y²+1)²=0
x²+y²+1=0
x²+y²=-1
∴此方程无解。
(5)x²-2xy+y²+(x-y)-6=0
(x-y)²+(x-y)-6=0
(x-y+3)(x-y-2)=0
x-y=-3 x-y=2
∴此方程无解。
你的题目有没有问题???
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(1)(x+y)(x+y-3)+2=0
(x+y)[(x+y)-3]+2=0
(x+y)^2-3(x+y)+2=0
(x+y-1)(x+y-2)=0
(2)(x-2)²-3(x-2)+2=0
[(x-2)-1][(x-2)-2]=0
(x-3)(x-4)=0
x=3,x=4
(3)(x+5)²-6(x+5)+9=0
[(x+5)-3]²=0
(x+2)²=0
x=-2
(4)(x²+y²+1)(x²+y²-3)=-4
[(x²+y²)+1][(x²+y²)-3]=-4
(x²+y²)²-2(x²+y²)-3=-4
(x²+y²)²-2(x²+y²)+1=0
[(x²+y²)-1]²=0
x²+y²-1=0
(5)x²-2xy+y²+(x-y)-6=0
(x-y)²+(x-y)-6=0
[(x-y)-2][(x-y)+3]=0
(x-y-2)(x-y+3)=0
(x+y)[(x+y)-3]+2=0
(x+y)^2-3(x+y)+2=0
(x+y-1)(x+y-2)=0
(2)(x-2)²-3(x-2)+2=0
[(x-2)-1][(x-2)-2]=0
(x-3)(x-4)=0
x=3,x=4
(3)(x+5)²-6(x+5)+9=0
[(x+5)-3]²=0
(x+2)²=0
x=-2
(4)(x²+y²+1)(x²+y²-3)=-4
[(x²+y²)+1][(x²+y²)-3]=-4
(x²+y²)²-2(x²+y²)-3=-4
(x²+y²)²-2(x²+y²)+1=0
[(x²+y²)-1]²=0
x²+y²-1=0
(5)x²-2xy+y²+(x-y)-6=0
(x-y)²+(x-y)-6=0
[(x-y)-2][(x-y)+3]=0
(x-y-2)(x-y+3)=0
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(1)(x+y)(x+y-3)+2=0
设x+y=a,
a(a+3)+2=0
a²+3a+2=0
(a+1)(a+2)=0
a1=-1,a2=-2,x+y=-1或-2
(2)(x-2)²-3(x-2)+2=0
设x-2=a,a²-3a+2=0
(a-1)(a-2)=0,a1=1,a2=2
x-2=1或x-2=2,x1=3,x2=0
(3)(x+5)²-6(x+5)+9=0
设x+5=a,a²-6a+9=0
(a-3)²=0
a=3,x+5=3,x=-2
(4)(x²+y²+1)(x²+y²-3)=-4
设x²+y²=a,(a+1)(a-3)=-4
a²-2a+1=0
(a-1)=0
a=1,x²+y²=1
(5)x²-2xy+y²+(x-y)-6=0
化简:(x-y)²+(x-y)-6=0
设x+y=a,a²+a-6=0
(a+3)(a-2)=0
a1=-3,a2=2
x+y=-3或2
设x+y=a,
a(a+3)+2=0
a²+3a+2=0
(a+1)(a+2)=0
a1=-1,a2=-2,x+y=-1或-2
(2)(x-2)²-3(x-2)+2=0
设x-2=a,a²-3a+2=0
(a-1)(a-2)=0,a1=1,a2=2
x-2=1或x-2=2,x1=3,x2=0
(3)(x+5)²-6(x+5)+9=0
设x+5=a,a²-6a+9=0
(a-3)²=0
a=3,x+5=3,x=-2
(4)(x²+y²+1)(x²+y²-3)=-4
设x²+y²=a,(a+1)(a-3)=-4
a²-2a+1=0
(a-1)=0
a=1,x²+y²=1
(5)x²-2xy+y²+(x-y)-6=0
化简:(x-y)²+(x-y)-6=0
设x+y=a,a²+a-6=0
(a+3)(a-2)=0
a1=-3,a2=2
x+y=-3或2
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(1)(x+y)(x+y-3)+2=0
解:(x+y)²-3(x+y)+2=0
(x+y-2)(x+y-1)=0
x+y=2或x+y=1
(2)(x-2)²-3(x-2)+2=0
解:[(x-2)-2][(x-2)-1]=0
(x-4)(x-3)=0
x=4或x=3
(3)(x+5)²-6(x+5)+9=0
解:[(x+5)-3]²=0
(x+2)²=0
x=-2
(4)(x²+y²+1)(x²+y²-3)=-4
解:(x²+y²)²-2(x²+y²)-3+4=0
(x²+y²)²-2(x²+y²)+1=0
(x²+y²-1)²=0
x²+y²=1
(5)x²-2xy+y²+(x-y)-6=0
解:(x-y)²+(x-y)-6=0
(x-y+3)(x-y-2)=0
x-y=-3或x-y=2
解:(x+y)²-3(x+y)+2=0
(x+y-2)(x+y-1)=0
x+y=2或x+y=1
(2)(x-2)²-3(x-2)+2=0
解:[(x-2)-2][(x-2)-1]=0
(x-4)(x-3)=0
x=4或x=3
(3)(x+5)²-6(x+5)+9=0
解:[(x+5)-3]²=0
(x+2)²=0
x=-2
(4)(x²+y²+1)(x²+y²-3)=-4
解:(x²+y²)²-2(x²+y²)-3+4=0
(x²+y²)²-2(x²+y²)+1=0
(x²+y²-1)²=0
x²+y²=1
(5)x²-2xy+y²+(x-y)-6=0
解:(x-y)²+(x-y)-6=0
(x-y+3)(x-y-2)=0
x-y=-3或x-y=2
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