If x/y + y/x = -1, (x, y ≠ 0), the value of x³ - y³ is
a. 1
b. -1
c. 0
d. 1/2

Solution:

We know that

x³ - y³ = (x - y) (x² + xy + y²) …. (1)

It is given that

x/y + y/x = -1

By further simplification we can write it as

(x² + y²)/ xy = -1

x² + y² = -xy

By adding xy on both sides

x² + y² + xy = -xy + xy

x² + y² + xy = 0 …. (2)

By substituting (2) in (1)

x³ - y³ = (x - y) x 0

x³ - y³ = 0

Therefore, the value of x³ - y³ 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 x³ - y³ 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 x³ - y³ is 0

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