已知:x+1/x=3,求x³+1/x³的值

已知:x+1/x=3,求x³+1/x³的值
已知:x+1/x=3,求x³+1/x³的值

已知:x+1/x=3,求x³+1/x³的值
x³+1/x³
=(x+1/x)(x²-1+1/x²)
=3(x²-1+1/x²)
=3(x²+2+1/x²-3)
=3[(x+1/x)²-3]
=3*[3²-3]
=3*6
=18

x^3+1/x^3=(x+1/x)[x^2- x乘(1/x )+(1/x)^2]=3[(x^2+(1/x)^2-1]=3[(x+1/x)^2-3]=3(3^2-3)=18