Question

if a/b +b/a = -1 then (a cube - b cube) = ?

Answer 1

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just substituted x=a y=b
hope this helps you.
Just a minor error

Answer 2

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a/b+b/a = -1
=( a^2 + b ^2 ) / ab = -1
= ( a^2 + b^2 + ab) = 0

a^3 - b^3 = (a-b)(a^2 + b^2 + ab)

so;

a^3 - b^3 = (a-b) . (0)
a^3 - b^3 = 0