若m²+n²-m-4n+4¼=0,求m的n次方-mn的值

若m²+n²-m-4n+4¼=0,求m的n次方-mn的值
若m²+n²-m-4n+4¼=0,求m的n次方-mn的值

若m²+n²-m-4n+4¼=0,求m的n次方-mn的值
m²+n²-m-4n+4¼=0
m²-m+1/4+n²-4n+4=0
(m-1/2)²+(n-2)²=0
m-1/2=0 m=1/2
n-2=0 n=2
m^n-mn
=(1/2)²-2(1/2)
=1/4-1
=-3/4

m²+n²-m-4n+4¼=0
(m²-m+1/4)+(n²-4n+4)=0
(m-1/2)²+(n-2)²=0
m-1/2=0
n-2=0
∴m=1/2 n=2
m^n-mn-(1/2)²-1/2×2=1/4-1=-3/4

(m-1/2)^2+(n-2)^2=0
m=1/2 n=2
m^(n)-mn=1/4-1=-3/4