Question

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

Answer 1

Step-by-step explanation:

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

Answer 2

Answer:

x/y +y/x = 1

On simplification

x² + y² = xy

➙ x² + y² - xy = 0

So

x³ + y³

= (x + y) ( x² + y² - xy)

= (x + y) × 0

= 0