Question

if a+1/a= 17/4 find (a-1/a)

Answer 1

take square both side  

( a + 1/a )^2 = (17/4)^2

a^2 + 1/(a)^2 + 2 = 289/16

subtract 4 from both side

a^2 + 1/a^2 - 2 = 225/16

we can write above equation like  

(a-1/a)^2 = (15/4)^2

so

a - 1/a = 15/4.