一元二次方程ax平方+bx+c的解x=-(b+或-根号b平方-4ac)/2a这个推理怎么来的,
人气:168 ℃ 时间:2020-01-29 07:38:56
解答
ax^2+bx+c=0
两边同时除以a得
x^2+(b/a)x+c/a=0
变为标准方程:
x^2+2(b/2a)x+c/a=0
然后变换得:
(x+b/2a)^2+c/a-b^2/4a^2=0
再移项得:
(x+b/2a)^2=b^2/4a^2-c/a
把右边通分得:
(x+b/2a)^2=(b^2-4ac)/4a^2
解方程得:
x+b/2a=[+(-)根号下b^2-4ac]/2a
故:
x=[-b+(-)根号下b^2-4ac]/2a
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