已知a²-5a+1=0,求a-1/a的值

已知a²-5a+1=0,求a-1/a的值
已知a²-5a+1=0,求a-1/a的值

已知a²-5a+1=0,求a-1/a的值
a² - 5a + 1 = 0
根据方程式,
x = [-b ± √(b² - 4ac)] / 2a
a = [5 ± √(25 - 4)] / 2
a = (5 ± √21) / 2
当 a = (5 + √21) / 2
(a - 1)/a
= {[(5 + √21) / 2] - 1} / [(5 + √21) / 2]
= (3 + √21) / (5 + √21)
= 0.79
当 a = (5 - √21) / 2
(a - 1)/a
= {[(5 - √21) / 2] - 1} / [(5 - √21) / 2]
= (3 - √21) / (5 - √21)
= -3.79