Question

若a方-3a+1=0则a方+a方分之1等于

已知a方-3a+1=0,则a方+a方分之1=___.
若a分之1+b分之1=6÷(a+b),则a分之b+b分之a的值等于( )
A.-4 B.4 C.-2 D.2

Answer 1

a方-3a+1=0
两边同时除以a得
a+1/a=3
两边同时平方得
a^2+1/(a^2)+2=9
a^2+1/(a^2)=7
1/a+1/b=6/(a+b)
(a+b)/ab=6/(a+b)
(a+b)^2=6ab
a^2+2ab+b^2=6ab
a^2+b^2=4ab
(a^2+b^2)/ab=4
a/b+b/a=4