Question

a+1/a = 3, find a-1/a and a^3-1/a^3

Answer 1

Step-by-step explanation:

Solution: (a+1)/a = 3

=> a+1 = 3a

=> 1 = 3a - a = 2a => a = 1/2.

Then, 1). a-1/a

= (1/2)-1/(1/2) = {(1 - 2)/2}/(1/2) = (-1/2)/(1/2) = -1

2). a^3-1/a^3

= (1/2)^3-1/(1/2)^3 = {(1/8)-1}/(1/8) = {(1 - 8)/8}/(1/8)

= (-7/8)/(1/8) = -7