Question

用公式法解(m^2-1)x^2-2mx-(m^2-4)=0(m为常数,且m不等于正负1）

Answer 1

(m^2-1)x^2-2mx-(m^2-4)=0

△=4m^2+4(m^2-1)(m^2-4)=4m^2+4(m^4-5m^2+4)=4(m^2-2)^2

x1=(2m+√△)/[2(m^2-1)]=[2m+2(m^2-2)]/(2m^2-2)=(m^2+m-2)/(m^2-1)=(m+2)(m-1)/(m+1)(m-1)=(m+2)/(m+1)

x2=(2m-2(m^2-2))/2(m^2-1)=(m-m^2+2)/(m^2-1)=-(m-2)(m+1)/(m+1)(m-1)=(2-m)/(m-1)