若实数x满足x²-5x-1=0则x²+x+1/x²-1/x= x²-1/x²=_数学解答

若实数x满足x²-5x-1=0则x²+x+1/x²-1/x= x²-1/x²=

人气：311 ℃　时间：2020-03-23 04:41:46

解答

x² - 5x - 1 = 0x² - 1 = 5xx - 1/x = 5x² +x + 1/x² - 1/x= (x²+ 1/x²) + (x - 1/x)= (x - 1/x)²+2 +(x - 1/x)= 5²+2+5= 32(x + 1/x)²= (x - 1/x)² + 4= 29x + ...