If xy+yx=−1 (x,y≠0), find the value of x3−y3
xy+yx=−1
⇒x2+y2xy=−1
⇒x2+y2=−1xy
⇒x2+y2+xy=0…(i)
Using the identity, x3−y3=(x−y)(x2+xy+y2)…(ii)
on putting the value of equation (i) in equation (ii), we get
∴x3−y3=0