Question

if x/y+y/x=-1(xy is not equals to 0) find the value of x^3-y^3​

Answer 1

Step-by-step explanation:

If x/y + y/x = -1 (x, y are not equal to zero), then what is x^3-y^3 equal to?

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First, we note that

x3−y3=(x−y)(x2+xy+y2)

Now, if xy+yx=−1 , then, by getting a common denominator, we find that

x2+y2xy=−1

Multiply through by xy :

x2+y2=−xy

bring all terms to the left:

x2+xy+y2=0

Hence,

x3−y3=(x−y)(x2+xy+y2)=(x−y)⋅0=0