solve this using expansions
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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
(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
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