已知实数m,n(m>n)是方程x2-2
|
∵方程x2-2
x+2=0的二次项系数a=1,一次项系数b=-23
,常数项c=2,3
∴b2-4ac=(-2
)2-4×1×2=4,3
∴x=-b± b2-4ac 2a
=2
±3 4 2×1
=
±1,3
∴m=
+1,n=3
-1;3
∴
+n m
=m n
+n2 mn m2 mn
=(
-1)2+(3
+1)23 (
+1)(3
-1)3
=(
-1)2+(3
+1)23 (
+1)(3
-1)3
=8 2
=4.