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)