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

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

若实数x满足x²-5x-1=0则x²+x+1/x²-1/x= x²-1/x²=
x² - 5x - 1 = 0
x² - 1 = 5x
x - 1/x = 5
x² +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
= 29
x + 1/x = ±√29
x² - 1/x²
= (x+ 1/x)(x - 1/x)
= ±5√29