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# If x/y + y/x = -1, (x, y ≠ 0), the value of x^{3} - y^{3} is

a. 1

b. -1

c. 0

d. 1/2

**Solution:**

We know that

x^{3} - y^{3} = (x - y) (x^{2} + xy + y^{2}) …. (1)

It is given that

x/y + y/x = -1

By further simplification we can write it as

(x^{2} + y^{2})/ xy = -1

x^{2} + y^{2} = -xy

By adding xy on both sides

x^{2} + y^{2} + xy = -xy + xy

x^{2} + y^{2} + xy = 0 …. (2)

By substituting (2) in (1)

x^{3} - y^{3} = (x - y) x 0

x^{3} - y^{3} = 0

Therefore, the value of x^{3} - y^{3} is 0.

**✦ Try This: **If x + 1 is a factor of the polynomial 9x² + kx, then the value of k is

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 2

**NCERT Exemplar Class 9 Maths Exercise 2.1 Problem 19**

## If x/y + y/x = -1, (x, y ≠ 0), the value of x^{3} - y^{3} is a. 1, b. -1, c. 0, d. 1/2

**Summary:**

Like terms in polynomials are those terms which have the same variable and same power. Terms that have different variables and different powers are known as unlike terms. If x/y + y/x = -1, (x, y ≠ 0), the value of x^{3} - y^{3} is 0

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