Question

if m = a^⅓ + a^-⅓, prove that m³-3m = a+ ¹/a​

Answer 1

(a+b)³=a³+b³+3ab(a+b)

Hence,

m³=(a⅓+a-⅓)³=a+1/a+3(a⅓+a-⅓)

=a+1/a+3m

LHS, m³-3m=a+1/a+3m-3m

=a+1/a = RHS