x^3-3x+1=0,求x^3+1/x^3希望您能帮我解答a

Question

x^3-3x+1=0,求x^3+1/x^3
希望您能帮我解答
a

Answer 1

应该是x^2-3x+1=0吧x^2-3x+1=0x-3+1/x=0x+1/x=3(x+1/x)²=3²x²+1/x²+2=9x²+1/x²=7于是x³+1/x³=(x+1/x)(x²+1/x²-1)=3*（7-1）=18