Question

if a^2+1/a^2=18and a not equal to0 find (i)a-1/a (ii)a^3-1/a^3​

Answer 1

a^2+1/a^2=18

a²+(1/a²) -2 = 18-2

a²+(1/a²) -2a/a = 16

(a-1/a)² = 16

(a-1/a) = ±4

(ii)a^3-1/a^3

(a-1/a){ (a-1/a)² + 3a./a}

= ±4{ ( 16+3)

= ±4 × 19