帮解2题文字题

来源:百度知道 编辑:UC知道 时间:2024/09/24 14:34:50
已知x+1/x=7.(1)求x^2+1/x^2的值 (2)x-1/x的值

(1)将x+1/x=7两边平方得x^2+1/x^2=(x+1/x)^2-2=49-2=47

(2)由(1)得x^2+1/x^2-4=(x-1/x)^2=43,所以x-1/x=正负根号43

sorry

1. x^2+1/x^2=(x^2+1/x^2)^2-2* x^2 * 1/x^2=49-2=47
2. x-1/x=(x-1/x)(x+1/x)/(x+1/x)=x^2-1/x^2=[(x^2+1/x^2)^2-4* * x^2 * 1/x^2]/7=(49-4)/7=45/7

解:
x+1/x=7
x+1=7x
x=1/6
(1) (x^2+1)/x^2
=(1/36+1)/(1/36)
=7
(2) (x-1)/x
=(1/6-1)/(1/6)
=5