初二数学题-填空(1)若a+1/a=2,那么a^2+1/a^2=(),a^4+1/a^4=().(2)若a+1/a=3,a^2+1/a^2=(),a^4+1/a^4=().(3)若a+1/a=n,那么a^2+1/a^2=(),a^4+1/a^4=().
2019-04-18
初二数学题-填空
(1)若a+1/a=2,那么a^2+1/a^2=(___),a^4+1/a^4=(___).(2)若a+1/a=3,a^2+1/a^2=(___),a^4+1/a^4=(___).(3)若a+1/a=n,那么a^2+1/a^2=(___),a^4+1/a^4=(___).
优质解答
a+1/a=2
(a+1/a)^2=a^2+1/a^2+2=4
所以a^2+1/a^2=2
(a^2+1/a^2)^2=a^4+1/a^4+2=4
所以a^4+1/a^4=2
同理a+1/a=3
a^2+1/a^2=7
a^4+1/a^4＝47
若a+1/a=n
a^2+1/a^2=n^2-2
a^4+1/a^4=n^4-4n^2+2
a+1/a=2
(a+1/a)^2=a^2+1/a^2+2=4
所以a^2+1/a^2=2
(a^2+1/a^2)^2=a^4+1/a^4+2=4
所以a^4+1/a^4=2
同理a+1/a=3
a^2+1/a^2=7
a^4+1/a^4＝47
若a+1/a=n
a^2+1/a^2=n^2-2
a^4+1/a^4=n^4-4n^2+2