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)] / 2aa = [5 ± √(25 - 4)] / 2a = (5 ± √21) / 2当 a = (5 + √21) / 2(a - 1)/a= {[(5 + √21) / 2] - 1} / [(5 + √21) / 2]= (3 + √21) / (5 ...我已经知道答案了，而且我问的是是a-1/a 不是(a - 1)/a当 a = (5 + √21) / 2a - 1/a= [(5 + √21) / 2] - 1 / [(5 + √21) / 2]= [(5 + √21) / 2] - [2 / (5 + √21)]= (25 + 10√21 + 21 - 2) / 2(5 + √21)= (44 + 10√21) / 2(5 + √21)= 4.687 ( 3 d.p. )当 a = (5 - √21) / 2a - 1/a= [(5 - √21) / 2] - 1 / [(5 - √21) / 2]= [(5 - √21) / 2] - [2 / (5 - √21)]= (25 - 10√21 + 21 - 2) / 2(5 - √21)= (44 - 10√21) / 2(5 - √21)= -0.381 ( 3 d.p. )