Question

解关于x的一元二次方程mx²-（3m+2）x+2m+2=0(m＞0)

解mx²-（3m+2）x+2m+2=0(m＞0)

Answer 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

追问

不太满意 可以用公式法吗

追答

ax²+bx+c=0 a=m，b=-(3m+2)，c=2m+2
x=[-b±√(b²-4ac)]/(2a)
=[(3m+2)±√(3m+2)²-4m(2m+2)]/(2m)
=[3m+2±√(9m²+12m+4-8m²-8m)]/(2m)
=[3m+2±√(m²+4m+4)]/(2m)
=[3m+2±√(m+2)²]/(2m)
=[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

追问

第三行 √(3m+2)²错了 b不是等于=-(3m+2) please 求解 拜托了