Question

(m的平方-25)x的平方-2m平方x+m的平方=0 (m不等于正负5)

Answer 1

解：(m²-25)x²-2m²x+m²=0 ( m≠ ±5 )
a=m²-25 , b=-2m² , c=m²
△=b²-4ac
=(-2m²)²-4(m²-25)×m²
=4m^4-4m^4+100m²
=100m²
△≥0 , √△=√(100m²)=10|m|

当△﹥0, m≠0,且m≠±5时，方程有两个不相等的实数根
x=(-b±√△)/2a
=(2m²±10|m|)/[2(m²-25)]
=(m²±5|m|)/(m²-25)
x1=(m²+5|m|)/(m²-25)
x2=(m²-5|m|)/(m²-25)

当△=0, m=0时，方程有两个相等的实数根
x1=x2=0