用因式分解法解方程 (1)x²+x-6=0
(2)5x²-3x=x+1(3)x²-2x+5=0(4)x²+4x+8=4x+11(5)4x²-6x=0(6)x(2x-4)=5-...
(2)5x²-3x=x+1 (3)x²-2x+5=0 (4)x²+4x+8=4x+11
(5)4x²-6x=0 (6)x(2x-4)=5-8x(7)(4x+4)²=x(2x+1)
(8)3x(x+2)=5(x+2) (9)(3x+1)²-5=0 (10)2(x+2)=4(x+2)
(11)(x+1)²-3(x+1)+2=0 (12)x²+12x+27=0 展开
(5)4x²-6x=0 (6)x(2x-4)=5-8x(7)(4x+4)²=x(2x+1)
(8)3x(x+2)=5(x+2) (9)(3x+1)²-5=0 (10)2(x+2)=4(x+2)
(11)(x+1)²-3(x+1)+2=0 (12)x²+12x+27=0 展开
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(1)x²+x-6=0
(x-2)(x+3)=0
x=2或x=-3
(2)5x²-3x=x+1
5x²-4x-1=0
(5x+1)(x-1)=0
x=-1/5或x=1
(3)x²-2x+5=0
x²-2x+1+4=0
(x-1)²+4=0
因为(x-1)²>=0,(x-1)^2+4>0
所以方程无解
(4)x²+4x+8=4x+11
x²-3=0
(x-√3)(x+√3)=0
x=√3或x=-√3
(5)4x²-6x=0
2x(2x-3)=0
x(2x-3)=0
x=0或x=3/2
(6)x(2x-4)=5-8x
2x²-4x=5-8x
2x²+4x-5=0
x²+2x-5/2=0
x²+2x+1-7/2=0
(x+1)²-14/4=0
(x+1-√14/2)(x+1+√14/2)=0
x=-1+√14/2或x=-1-√14/2
(7)(4x+4)²=x(2x+1)
16x²+32x+16=2x²+x
14x²+31x+16=0
x²+31x/14+16/14=0
x²+31x/14+961/784-961/784+16/14=0
(x+31/28)²-961/784+896/784=0
(x+31/28)²-65/784=0
(x+31/28-√65/28)(x+31/28+√65/28)=0
x=-31/28+√65/28或x=-31/28-√65/28
(8)3x(x+2)=5(x+2)
3x(x+2)-5(x+2) =0
(x+2)(3x-5)=0
x=-2或x=5/3
(9)(3x+1)²-5=0
(3x+1-√5)(3x+1+√5)=0
x=(√5-1)/3或x=-(√5+1)/3
(10)2(x+2)=4(x+2)
2(x+2)=0
x+2=0
x=-2
(11)(x+1)²-3(x+1)+2=0
(x+1-2)(x+1-1)=0
x(x-1)=0
x=0或x=1
(12)x²+12x+27=0
(x+3)(x+9)=0
x=-3或x=-9
(13) x²+3=2√3x
x²-2√3x+3=0
(x-√3)²=0
x=√3
(14) x²+(5-√2)x-5√2=0
(x+5)(x-√2)=0
x=-5或x=√2
(x-2)(x+3)=0
x=2或x=-3
(2)5x²-3x=x+1
5x²-4x-1=0
(5x+1)(x-1)=0
x=-1/5或x=1
(3)x²-2x+5=0
x²-2x+1+4=0
(x-1)²+4=0
因为(x-1)²>=0,(x-1)^2+4>0
所以方程无解
(4)x²+4x+8=4x+11
x²-3=0
(x-√3)(x+√3)=0
x=√3或x=-√3
(5)4x²-6x=0
2x(2x-3)=0
x(2x-3)=0
x=0或x=3/2
(6)x(2x-4)=5-8x
2x²-4x=5-8x
2x²+4x-5=0
x²+2x-5/2=0
x²+2x+1-7/2=0
(x+1)²-14/4=0
(x+1-√14/2)(x+1+√14/2)=0
x=-1+√14/2或x=-1-√14/2
(7)(4x+4)²=x(2x+1)
16x²+32x+16=2x²+x
14x²+31x+16=0
x²+31x/14+16/14=0
x²+31x/14+961/784-961/784+16/14=0
(x+31/28)²-961/784+896/784=0
(x+31/28)²-65/784=0
(x+31/28-√65/28)(x+31/28+√65/28)=0
x=-31/28+√65/28或x=-31/28-√65/28
(8)3x(x+2)=5(x+2)
3x(x+2)-5(x+2) =0
(x+2)(3x-5)=0
x=-2或x=5/3
(9)(3x+1)²-5=0
(3x+1-√5)(3x+1+√5)=0
x=(√5-1)/3或x=-(√5+1)/3
(10)2(x+2)=4(x+2)
2(x+2)=0
x+2=0
x=-2
(11)(x+1)²-3(x+1)+2=0
(x+1-2)(x+1-1)=0
x(x-1)=0
x=0或x=1
(12)x²+12x+27=0
(x+3)(x+9)=0
x=-3或x=-9
(13) x²+3=2√3x
x²-2√3x+3=0
(x-√3)²=0
x=√3
(14) x²+(5-√2)x-5√2=0
(x+5)(x-√2)=0
x=-5或x=√2
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