x1+x2=(m-2)/(1/4)=4(m-2)
x1x2=m^2/(1/4)=4m^2
x1^2+x2^2=224
(x1+x2)^2-2x1x2=224
[4(m-2)]^2-2*4m^2=224
2(m-2)^2-m^2=28
m^2-8m-20=0
(m+2)(m-10)=0
m=-2,或10
m=10时,判别式=(10-2)^2-4*1/4*10^2＜0,舍去
∴m=-2
已知关于x的方程1/4x2-(m-2)x+m2=0
x1+x2=(m-2)/(1/4)=4(m-2)
x1x2=m^2/(1/4)=4m^2
x1^2+x2^2=224
(x1+x2)^2-2x1x2=224
[4(m-2)]^2-2*4m^2=224
2(m-2)^2-m^2=28
m^2-8m-20=0
(m+2)(m-10)=0
m=-2,或10
m=10时,判别式=(10-2)^2-4*1/4*10^2＜0,舍去
∴m=-2