利用一元二次方程的根的判断式,判断方程根的情况
(m²+1)x²-4mx+(m²+1)=0(m≠正负1)
人气:220 ℃ 时间:2020-01-12 19:31:13
解答
(m²+1)x²-4mx+(m²+1)=0
(m²+1)(x²-4mx/(m²+1)+4m²/(m²+1)²)-4m²/(m²+1)+(m²+1)=0
(m²+1)(x-2m/(m²+1))²=[4m²-(m²+1)²]/(m²+1)
(m²+1)(x-2m/(m²+1))²=(2m+m²+1)(2m-m²-1)/(m²+1)
(m²+1)(x-2m/(m²+1))²=(m+1)²(-(m-1)²)/(m²+1)=-(m+1)²(m-1)²/(m²+1)
因为m≠正负1
(m²+1)(x-2m/(m²+1))²=(m+1)²(-(m-1)²)/(m²+1)=-(m+1)²(m-1)²/(m²+1)
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