Question

利用一元二次方程的根的判断式,判断方程根的情况

Answer 1

（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)