若a2−3a+1+b2+2b+1=0,则a2+1/a2−|b|=_.

问题描述:

a2−3a+1
+b2+2b+1=0,则a2+
1
a2
−|b|
=______.

a2−3a+1
+b2+2b+1=0,
a2−3a+1
+(b+1)2=0,
∴a2-3a+1=0,b+1=0,
∴a+
1
a
=3,
∴(a+
1
a
2=32
∴a2+
1
a2
=7;
b=-1.
a2+
1
a2
−|b|
=7-1=6.
故答案为:6.