解下列题目(要有算式)已知x+1/x=3(1)x^3+1/x^3=?(2)x^5+1/x^5=?

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解下列题目(要有算式)已知x+1/x=3(1)x^3+1/x^3=?(2)x^5+1/x^5=?
解下列题目(要有算式)
已知x+1/x=3
(1)x^3+1/x^3=?
(2)x^5+1/x^5=?

解下列题目(要有算式)已知x+1/x=3(1)x^3+1/x^3=?(2)x^5+1/x^5=?
x+1/x=3
(x+1/x)^2=9
x^2+1/x^2+2=9
x^2+1/x^2=7
x^3+1/x^3=(x+1/x)(x^2+1/x^2-1)=3*(7-1)=18
(x^2+1/x^2)(x^3+1/x^3)
=x^5+x^2/x^3+x^3/x^2+1/x^5
=x^5+1/x^5+x+1/x
=x^5+1/x^5+3
=7*18
所以,x^5+1/x^5=123