Question

If x/y+y/x=-1;x,y not equal to zero then find the value of x^3-y^3

Answer 1

Given expression,
  x/y+y/x=-1
  =>x²+y²/xy=-1                      [ Since, L.C.M. of x and y =xy   ]
  =>x²+y²=-xy
  =>x²+y²+xy=0    ..................( Equation i )
  Now,
   formula of a³-b³=(a-b)(a²+ab+b²)
   applying this formula  to find x³+y³
  =>x³-y³=(x-y)(x²+xy+y²)
  By equation i, value of (x²+xy+y²)=0
=>x³-y³=(x-y)*0
=>x³-y³=0
      (Solved)