数学
解关于x的一元二次方程mx2-(3m 2)x 2m 2=0(m能用公式法吗?

2019-04-13

解关于x的一元二次方程mx2-(3m 2)x 2m 2=0(m
能用公式法吗?
优质解答
mx²-(3m+2)x+2m+2=0
x²-(3m+2)x/m+(2m+2)/m=0
x²-(3m+2)x/m=-(2m+2)/m
x²-(3m+2)x/m+(3m+2)²/(4m²)=(3m+2)²/(4m²)-4m(2m+2)/(4m²)
(x-3m+2)²=(9m²+12m+4)/(4m²)-(8m²+8m)/(4m²)
(x-3m+2)²=(9m²+12m+4-8m²-8m)/(4m²)
(x-3m+2)²=(m²+4m+4)/(4m²)
(x-3m+2)²=(m+2)²/(4m²)
x-3m+2=±(m+2)/(2m)
x=[3m+2±(m+2)]/(2m)
x1=(3m+2+m+2)/(2m)=(4m+4)/(2m)=(2m+2)/m
x2=(3m+2-m-2)/(2m)=(2m)/(2m)=1
mx²-(3m+2)x+2m+2=0
x²-(3m+2)x/m+(2m+2)/m=0
x²-(3m+2)x/m=-(2m+2)/m
x²-(3m+2)x/m+(3m+2)²/(4m²)=(3m+2)²/(4m²)-4m(2m+2)/(4m²)
(x-3m+2)²=(9m²+12m+4)/(4m²)-(8m²+8m)/(4m²)
(x-3m+2)²=(9m²+12m+4-8m²-8m)/(4m²)
(x-3m+2)²=(m²+4m+4)/(4m²)
(x-3m+2)²=(m+2)²/(4m²)
x-3m+2=±(m+2)/(2m)
x=[3m+2±(m+2)]/(2m)
x1=(3m+2+m+2)/(2m)=(4m+4)/(2m)=(2m+2)/m
x2=(3m+2-m-2)/(2m)=(2m)/(2m)=1
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