已知实数x满足x²-3x+1=0.求（1）x+ 1/x (2)x²+ 1/x² (3)x-1/x

题目

已知实数x满足x²-3x+1=0.求（1）x+ 1/x (2)x²+ 1/x² (3)x-1/x
已知实数x满足x²-3x+1=0.求（1）x+ 1/x (2)x²+ 1/x² (3)x-1/x

答案

x²-3x+1=0除以x得 x-3+1/x=0x+1/x=3(2)x²+ 1/x² =x²+2+1/x²-2=(x+1/x)²-2=3²-2=7(3)(x-1/x)²=(x+1/x)²-4=3²-4=5∴x-1/x=±√5