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

问题描述:

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

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