用配方法解一元二次方程 x²-x-1=0 y²-6y+6=0 x²+4x-3=0 3x²-4x=2 2x²+4x=3 2(x-1)²-(x+1)(1-x)=(x+2)² (2x-1)²-2(2x-1)=3
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![用配方法解一元二次方程 x²-x-1=0 y²-6y+6=0 x²+4x-3=0 3x²-4x=2 2x²+4x=3 2(x-1)²-(x+1)(1-x)=(x+2)² (2x-1)²-2(2x-1)=3](/uploads/image/z/804773-29-3.jpg?t=%E7%94%A8%E9%85%8D%E6%96%B9%E6%B3%95%E8%A7%A3%E4%B8%80%E5%85%83%E4%BA%8C%E6%AC%A1%E6%96%B9%E7%A8%8B+x%26%23178%3B-x-1%3D0+y%26%23178%3B-6y%2B6%3D0+x%26%23178%3B%2B4x-3%3D0+3x%26%23178%3B-4x%3D2+2x%26%23178%3B%2B4x%3D3+2%28x-1%29%26%23178%3B-%EF%BC%88x%2B1%EF%BC%89%EF%BC%881-x%EF%BC%89%3D%28x%2B2%29%26%23178%3B+%EF%BC%882x-1%EF%BC%89%26%23178%3B-2%EF%BC%882x-1%EF%BC%89%3D3)
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用配方法解一元二次方程 x²-x-1=0 y²-6y+6=0 x²+4x-3=0 3x²-4x=2 2x²+4x=3 2(x-1)²-(x+1)(1-x)=(x+2)² (2x-1)²-2(2x-1)=3
用配方法解一元二次方程 x²-x-1=0 y²-6y+6=0 x²+4x-3=0 3x²-4x=2 2x²+4x=3 2(x-1)²-(x+1)(1-x)=(x+2)² (2x-1)²-2(2x-1)=3
用配方法解一元二次方程 x²-x-1=0 y²-6y+6=0 x²+4x-3=0 3x²-4x=2 2x²+4x=3 2(x-1)²-(x+1)(1-x)=(x+2)² (2x-1)²-2(2x-1)=3
配方法的解题步骤是:
(1)常数项右移;(2)除以二次项系数;(3)配方:都加一次项系数一半的平方;(4)直接开平方求解.
以最麻烦的题目为例:2x²+4x=3 x²+2x=3/2 x²+2x+1=3/2+1 (x+1)²=5/2 x+1=±(根10)/2
∴x1=-1+(根10)/2 x2=-1-(根10)/2
至于最后两个题目,可以先展开再合并,最后再用配方法来解