Question

x/y + y/x = -1 find the value of x³ - y³

Answer 1

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IT IS YOUR ANSWER..

Answer 2

Given,

x/y + y/x = -1

To find,

The value of x³ - y³.

Solution,

We can easily solve this problem by following the given steps.

According to the question:

We have the following expression:

x/y + y/x = -1

Now, take the LCM of y and x and add the fractions:

(x²+y²)/xy = -1

Using the cross multiplication method:

(x²+y²) = -xy ---(1)

We know that the following identity is used to expand x³ - y³:

(x³-y³) = (x-y) (x²+xy+y²)

Now, put the value of (x²+y²) from equation 1,

(x³-y³) = (x-y) (-xy+xy)

(x³-y³) = (x-y) 0

(We know that if we multiply any number with 0 then the result is always 0.)

(x³-y³) = 0

Hence, the value of x³ - y³ is 0.