若a+b+c=0,1/a+1+1/b+2+1/c+3=0,那么(a+1)2+(b+2)2+(c+3)2=_.
问题描述:
若a+b+c=0,
+1 a+1
+1 b+2
=0,那么(a+1)2+(b+2)2+(c+3)2=______. 1 c+3
答
∵a+b+c=0,
∴(a+1)+(b+2)+(c+3)=6,
两边平方得(a+1)2+(b+2)2+(c+3)2+2[(a+1)(b+2)+(a+1)(c+3)+(b+2)(c+3)]=36,
又由
+1 a+1
+1 b+2
=0去分母,得1 c+3
(b+2)(c+3)+(a+1)(c+3)+(a+1)(b+2)=0,
∴(a+1)2+(b+2)2+(c+3)2=36.
故答案为:36.