Question

solve this using expansions

Answer 1

a^2+1/a^2=18
(a^4+a^2)/a^2=18
a^2(a^2+1)/a^2=18
a^2+1=18
a^2=17
a=√17

a-1/a=√17-1/√17
=(17-1)/√17
=16/√17

a^3-1/a^3=(√17)^3-1/(√17)^3
=17√17-1/17√17
=(4913-1)/17√17
=4912/17√17