Question

已知a²－3a＋1＝0，求a＋a分之1，a²＋a²分之1和﹙a－a分之1﹚²的值

Answer 1

a�0�5-3a+1=0
a�0�5+1=3a
等号两边同除以a得：a+1/a=3
上式等号两边同时平方得：a�0�5+1/a�0�5=3�0�5-2=7
上式变为：a�0�5-2+1/a�0�5=7-2=5
上式等号两边同时开方得：a-1/a=±√5

Answer 2

解：因为（∵）a�0�5-3a+1=0，所以（∴）a-3+1/a=0，a+1/a=3
又∵（a+1/a）�0�5=a�0�5+2·a·1/a+1/a�0�5=3�0�5
∴a�0�5+2+1/a�0�5=9，a�0�5+1/a�0�5=9-2=7