If x/y+y/x=1 (x, y≠0) , find the value of x3 + y3.

Answer:     the value of x³ + y³ is 0.======    combine the two fractions on the left-hand side of the equation.  get a common denominator. the lcd between y and x is xy.multiply numerator and denominator of x/y by x:     multiply numerator and denominator of y/x by y:     multiply both sides of equation by xy:     subtract both sides by xy:     now x² - xy + y² is a part of a factoring identity. (the question asking for the value of x³ + y³  also hints at the use of this identity.)this factoring identity is the sum of cubes identity, which is as follows:     notice how we have x² - xy + y² in that factoring identity.  if you multiply x² - xy + y² by x+y, you get x³ + y³.therefore, with our equation, multiply both sides by (x+y):     the right-hand side stays 0.the left-hand side can change, according to the identity, into x³ + y³ becausex³ + y³ = (x+y)(x² - xy + y²)    the value of x³ + y³ is 0.