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Assume that the reciprocal of m+2 is
1
m
+2，them the value of m2+
1
m2
 is
 
．
（英漢詞典：to assume假設(shè)；reciprocal倒數(shù)；value值）
分析：根據(jù)提示，得m+2的倒數(shù)為
1
m
+2，求m2+
1
m2
 的值，則先列式求得m，再代入求出m2+
1
m2
 的值即可．
解答：解：根據(jù)題意得，（m+2）×（
1
m
+2）=1，
（1+2m）（m+2）=m，
m2+2m+1=0，
∴m=-1，
∴m2+
1
m2
=（-1）2+
1
(-1)2

=1+1
=2，
故答案為2．
點(diǎn)評(píng)：本題考查了分式的混合運(yùn)算以及完全平方公式，兩個(gè)數(shù)的乘積為1，則這兩個(gè)數(shù)互為倒數(shù)．
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