Question

If a/b + b/a = -1, then find a3-b3.

Answer 1

a/b + b/a = -1 a^2+b^2/ab= -1 a^2+b^2= -ab......... eq 1 a^3-b^3= (a-b)(a^2+ab+b^2) = (a-b)(-ab+ab) from eq 1 =(a-b) × 0 =0

Answer 2

:a/b + b/a = -1

a^2+b^2/ab= -1

a^2+b^2= -ab......... eq 1

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

= (a-b)(-ab+ab) ....... from eq 1

=(a-b) × 0 =0