1.用公式法解下列方程:(1)x²-2根号3x+3=0 (2)2x²-2x+1=02.不解方程,判断下列方程根的情况:(1)3x²-x+1=3x(2)5(x²+1)=7x (3)3x²-4根号3x=-4 (4)x²-(k+2)x+(k-1)=0
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![1.用公式法解下列方程:(1)x²-2根号3x+3=0 (2)2x²-2x+1=02.不解方程,判断下列方程根的情况:(1)3x²-x+1=3x(2)5(x²+1)=7x (3)3x²-4根号3x=-4 (4)x²-(k+2)x+(k-1)=0](/uploads/image/z/380460-12-0.jpg?t=1.%E7%94%A8%E5%85%AC%E5%BC%8F%E6%B3%95%E8%A7%A3%E4%B8%8B%E5%88%97%E6%96%B9%E7%A8%8B%EF%BC%9A%EF%BC%881%EF%BC%89x%26%23178%3B-2%E6%A0%B9%E5%8F%B73x%2B3%3D0+%EF%BC%882%EF%BC%892x%26%23178%3B-2x%2B1%3D02.%E4%B8%8D%E8%A7%A3%E6%96%B9%E7%A8%8B%2C%E5%88%A4%E6%96%AD%E4%B8%8B%E5%88%97%E6%96%B9%E7%A8%8B%E6%A0%B9%E7%9A%84%E6%83%85%E5%86%B5%3A%281%293x%26%23178%3B-x%2B1%3D3x%EF%BC%882%EF%BC%895%EF%BC%88x%26%23178%3B%2B1%EF%BC%89%3D7x+%EF%BC%883%EF%BC%893x%26%23178%3B-4%E6%A0%B9%E5%8F%B73x%3D-4+%EF%BC%884%EF%BC%89x%26%23178%3B-%EF%BC%88k%2B2%29x%2B%28k-1%29%3D0)
1.用公式法解下列方程:(1)x²-2根号3x+3=0 (2)2x²-2x+1=02.不解方程,判断下列方程根的情况:(1)3x²-x+1=3x(2)5(x²+1)=7x (3)3x²-4根号3x=-4 (4)x²-(k+2)x+(k-1)=0
1.用公式法解下列方程:(1)x²-2根号3x+3=0 (2)2x²-2x+1=0
2.不解方程,判断下列方程根的情况:(1)3x²-x+1=3x(2)5(x²+1)=7x (3)3x²-4根号3x=-4
(4)x²-(k+2)x+(k-1)=0
1.用公式法解下列方程:(1)x²-2根号3x+3=0 (2)2x²-2x+1=02.不解方程,判断下列方程根的情况:(1)3x²-x+1=3x(2)5(x²+1)=7x (3)3x²-4根号3x=-4 (4)x²-(k+2)x+(k-1)=0
(1)x²-2根号3x+3=0
a=1 b=-2√3 c=3
b²-4ac=12-12=0
代入求根公式得
x=(2√3±√0)/2
x1=x2=√3
(2)2x²-2x+1=0
a=2 b=-2 c=1
b²-4ac=4-8<0
所以原方程无解
2.不解方程,判断下列方程根的情况:
(1)3x²-x+1=3x
3x²-4x+1=0
b²-4ac=16-12=4>0
有2个不相等的实数根
(2)5(x²+1)=7x
5x²-7x+5=0
b²-4ac=49-100<0
所以原方程无解
(3)3x²-4根号3x=-4
3x²-4√3x+4=0
b²-4ac=48-48=0
有2个相等的实数根
(4)x²-(k+2)x+(k-1)=0
b²-4ac=(k+2)²-4(k-1)=k²+4k+4-4k+4=k²+8>0
有2个不相等的实数根