Question

If x/y+y/x=-1(x,ynot equal 0), then find the value of x³-y³


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Answer 1

Step-by-step explanation:

x/y + y/x = (-1)

=> x² + y²/xy = (-1)

=> x² + y² = -xy

=> x² + y² + xy = 0 ---------(i)

x³ - y³ = (x-y)(x²+y²+xy)

{we got from equation (i)}

x² + y² + xy = 0

=> (x-y)(0)

=> 0

Answer 2

Answer:

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