一道初二分式计算已知a+1/a=2求1.a^2+1/(a^2)2.a^3+1/(a^3)3.a^4+1/(a^4)

Question

一道初二分式计算
已知a+1/a=2求
1.a^2+1/(a^2)
2.a^3+1/(a^3)
3.a^4+1/(a^4)

Answer 1

1.a^2+1/(a^2)=(a+1/a)^2-2=2^2-2=2
2.a^3+1/(a^3) =(a+1/a)[a^2+1/(a^2)-1]=2*(2-1)=2
3.a^4+1/(a^4)=[a^2+1/(a^2)]^2-2=2^2-2=2