已知x+1⼀x=3,求x^2+1⼀x^2,x^3+1⼀x^3,x^4+1⼀x^4

2025-06-23 07:58:32
推荐回答(1个)
回答1:

1、x+1/x=3
(x+1/x)²=3²
x²+1/x²+2=9
x²+1/x²=7
2、(x+1/x)(x²+1/x²)=3×7
x³+1/x+x+1/x³=21
x³+1/x³+3=21
x³+1/x³=18
3、(x²+1/x²)²=7²
x^4+1/x^4+2=49
x^4+1/x^=47