Question

已知x+1/x=2,x^2+1/x^2=3,求x^3+1/x^3的值

Answer 1

解：x^3+1/x^3
=(x+1/x)(x^2-1+1/x^2)
=2×(3-1)
=4.

Answer 2

题目表达不清，是不是（x+1）/x=2,（x^2+1）/x^2=3,求（x^3+1）/x^3的值
如果是这样解：x^3+1/x^3
=(x+1/x)(x^2-1+1/x^2)
=2×(3-1)
=4.
那么：x+1/x=2,两边同时平方，x^2+2+1/x^2=4 x^2+1/x^2=2与x^2+1/x^2=3有矛盾。