若a,b都是有理数,且a2-2ab+2b2+4a+8=0,则ab=( ) A.-8 B.8 C.32 D.2004
问题描述:
若a,b都是有理数,且a2-2ab+2b2+4a+8=0,则ab=( )
A. -8
B. 8
C. 32
D. 2004
答
a2-2ab+2b2+4a+8=2a2-4ab+4b2+8a+16=(a2-4ab+4b2)+(a2+8a+16)=(a-2b)2+(a+4)2=0,
∴a-2b=0且a+4=0,
解得:a=-4,b=-2,
则ab=8.
故选B.