Question

if x/y + y/x = -1
then find x^3 - y ^3

Answer 1

We know that,
x³-y³=(x-y)(x²+xy+y²)........................1
Given that,
x/y+y/x=-1

(x²+y²)/xy=-1

x²+y²=-xy

x²+y²+xy=0

(x²+xy+y²)=0
Multyplying by (x-y) on both sides we get,
(x-y)(x²+xy+y²)=(x-y)×0
By eq1 we get,
x³-y³=0

Hence x³-y³=0.

Answer 2

Given:

An equation consisting of two variables x and y. (x/y) + (y/x) = -1.

To Find:

The value of x³-y³.

Solution:

The given problem can be solved using the formula of a³ - b³.

1. The given equation is,

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

2. The above equation can also be written as,

=> (x * x + y * y)/xy = -1, (Transfer the term xy to the Right Hand side).

=> x²  + y² = -xy,

=> x² + y² + xy = 0. ( Conisder as equation 1).

3. The value of x³ - y³ is to be calculated, x³ - y³ can be expanded as,

=> x³ - y³ = ( x - y ) * ( x² + y² + xy ),

From equation 1, the value of  x² + y² + xy is 0. Substitute the value in the above equation.

=> x³ - y³ = ( x - y ) * ( 0 ),

=> x³ - y³ = 0.

Therefore, the value of x³ - y³ is 0.