x^2-√2x-1/4=0

来源：百度知道编辑：UC知道时间：2024/05/17 03:22:50

急急急。配方解答

x^2-√2x-1/4=0
x^2-2*(√2/2)x-1/4=0
x^2-2*(√2/2)x+(√2/2)^2-(√2/2)^2-1/4=0
[x-(√2/2)]^2=3/4
[x-（√2/2)]^2=(√3/2)^2
x-（√2/2)=√3/2或-√3/2
所以x1=(√3+√2)/2,x2=(√2-√3)/2

原式=(x-√2/2)^2-3/4
=(x-√2/2+√3/2)(x-√2/2-√3/2)

(x^2-√2/2)^2=3/4

x^2-√2x-1/4=0
x^2-√2x+1/2＝1/4+1/2
(x-√2/2)^2＝3/4
x-√2/2＝±√3/2
x＝(√2±√3)/2

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