Question

已知a+1/a=3，求下列式子的值

(1)a^2+1/a^2
(2)a^3+1/a^3
(3)a^4+1/a^4

Answer 1

（1）
把a+1/a=3两边同时平方：
a²+2+1/a²=9
∴a²+1/a²＝7
（2）
(a²+1/a²)(a+1/a)=3*7
∴a^3+1/a^3+a+1/a=21
∴a^3+1/a^3=21-3=18
（3）把a²+1/a²＝7两边同时平方：
a^4+1/a^4+2＝49
a^4+1/a^4＝47

Answer 2

a+1/a=3
(a+1/a)^2=a^2+1/a^2+2=9
(1)a^2+1/a^2=9-2=7

(2)a^3+1/a^3=(a+1/a)(a^2+1/a^2-1)=3(7-1)=18

a^2+1/a^2=7
(a^2+1/a^2)^2=a^4+1/a^4+2=49
(3)a^4+1/a^4=49-2=47

Answer 3

(1)a^2+1/a^2= 7
(2)a^3+1/a^3=18
(3)a^4+1/a^4=47

Answer 4

a+1/a=3 a=0.5 你算出来就行了

Answer 5

(1)a^2+1/a^2
=(a+1/a)^2-2
=9-2
=7

(2)a^3+1/a^3
=(a+1/a)(a^2-1+1/a^2)
=3*(7-1)
=18

(3)a^4+1/a^4
=(a^2+1/a^2)^2-2
=49-2
=47