设x,y为实数,5x2+4y2-8xy+2x+4的最小值为( )
A.1
B.2
C.3
D.5
∵5x2+4y2-8xy+2x+4
=(x2+2x+1)+(4x2-8xy+4y2)+3
=4(x-y)2+(x+1)2+3,
又∵4(x-y)2和(x+1)2的最小值是0,
∴5x2+4y2-8xy+2x+4的最小值为3.
故选C.
设x,y为实数,5x2+4y2-8xy+2x+4的最小值为( )
A.1
B.2
C.3
D.5
∵5x2+4y2-8xy+2x+4
=(x2+2x+1)+(4x2-8xy+4y2)+3
=4(x-y)2+(x+1)2+3,
又∵4(x-y)2和(x+1)2的最小值是0,
∴5x2+4y2-8xy+2x+4的最小值为3.
故选C.