设两个实数根为x1、x2,由韦达定理,可得
x1+x2=-2(m-2) ,x1x2=m²+4
x1²+x2²=(x1+x2)²-2x1x2
=[-2(m-2) ]²-2(m²+4)
=4m²-16m+16-2m²-8
=2m²-16m+8
由题可得：
(x1²+x2²)-x1x2=84
2m²-16m+8-(m²+4)=84
2m²-16m+8-m²-4=84
m²-16m-80=0
(m+4)(m-20)=0
m+4=0 或 m-20=0
m=-4 或 m=20
方程有两个实数根,则△≥0
△=[ 2(m-2) ]²-4(m²+4)
=4m²-16m+16-4m²-16
=-16m
-16m≥0
m≤0
所以 m=-4