早教吧作业答案频道 -->数学-->
高一数学数学请详细解答,谢谢!(115:53:45)x2+3x+1=0,求x3+1/x3与x7+1/x7的值.
题目详情
高一 数学 数学 请详细解答,谢谢! (1 15:53:45)
x2+3x+1=0,求x3+1/x3与x7+1/x7的值.
x2+3x+1=0,求x3+1/x3与x7+1/x7的值.
▼优质解答
答案和解析
x2+3x+1=0
两边同时除以 x
x+3+1/x=0
x+1/x=-3
两边平方得
x2+2+1/x2=9
x2+1/x2=7
二边平方得:
x4+2+1/x4=49
x4+1/x4=47
(x+1/x)(x2+1/x2)=x3+1/x+x+1/x3
-3*7=x3+1/x3-3
故x3+1/x3=-21+3=-18
(x3+1/x3)(x4+1/x4)=x7+1/x+x+1/x7
-18*47=x7+1/x7-3
故x7+1/x7=-846+3=-843
两边同时除以 x
x+3+1/x=0
x+1/x=-3
两边平方得
x2+2+1/x2=9
x2+1/x2=7
二边平方得:
x4+2+1/x4=49
x4+1/x4=47
(x+1/x)(x2+1/x2)=x3+1/x+x+1/x3
-3*7=x3+1/x3-3
故x3+1/x3=-21+3=-18
(x3+1/x3)(x4+1/x4)=x7+1/x+x+1/x7
-18*47=x7+1/x7-3
故x7+1/x7=-846+3=-843
看了 高一数学数学请详细解答,谢谢...的网友还看了以下：