Question

If x/y + y/x = -1 where x is not equal to 0 and y is not equal to zero , then find the value of x^3 - y^3​

Answer 1

Step-by-step explanation:

Given :-

x/y + y/x = -1 where x ≠0 and y ≠ 0

To find :-

Find the value of x³ - y³ ?

Solution :-

Given that :

x/y + y/x = -1

Where, x ≠ 0 and y ≠ 0

=>[(x×x)+(y×y)]/(xy) = -1

=> (x²+y²)/(xy) = -1

=> x²+y² = -1(xy)

=> x²+y² = -xy

=> x²+y²+xy = 0 -----------(1)

Now,

The value of x³-y³

We know that

x³-y³ = (x-y)(x²+xy+y²)

=> x³-y³ = (x-y)(0)

From (1)

=> x³-y³ = 0

Therefore, x³-y³ = 0

Answer:-

The value of x³-y³ for the given problem is 0

Used formulae:-

• x³-y³ = (x-y)(x²+xy+y²)