a+1/a=5
兩邊平方
a^2+2*a*1/a+1/a^2=5^2
a^2+2+1/a^2=25
a^2+1/a^2=23
(a^4+a^2+1)/a^2
=a^2+1+1/a^2
=23+1
=24
x/(x^2-x+1)=7
x=7x^2-7x+7=0
7x^2-8x+7=0
兩邊除以7x
x-8/7+1/x=0
x+1/x=8/7
兩邊平方
x^2+2+1/x^2=64/49
x^2+1/x^2=-34/49
x^2/(x^4+x^2+1)
上下除以x^2
=1/(x^2+1+1/x^2)
=1/(-34/49+1)
=49/15
a^2-3a+1=0
a^2+1=3a
a+1/a=3
a^2+2+1/a^2=9
a^2+1/a^2=7
a^2/(a^4+a^2+1)
上下除以a^2
=1/(a^2+1+1/a^2)
=1/(7+1
=1/8
x+1/x
和第三題一樣
把a換成x
結(jié)果=1/8
1/a+1/b=1/(a+b)
(a+b)/ab=1/(a+b)
對角相乘
(a+b)^2=ab
a^2+2ab+b^2=ab
a^2+b^2=-ab
b/a+a/b
=(a^2+b^2)/ab
=-ab/ab
=-1