Question

please refer to the attached question.​

Answer 1

Answer:

Check the attachment for the answer.

Answer 2

Question :-

If (x/y) + (y/x)= - 1 (x, y ≠ 0) then the value of x³ - y³ is

(A) 3

(B) - 3

(C) 0

(D) 1

Answer :-

(C) 0

Explanation :-

$\mathsf{ \dfrac{x}{y} + \dfrac{y}{x} = - 1 }$

Multiplying throughtout by xy

$\mathsf{ \implies \dfrac{x}{y}(xy) + \dfrac{y}{x} (xy)= - 1(xy) }$

$\mathsf{ \implies x^2 + y^2= -xy }$

We know that

x³ - y³ = (x - y)(x² + y² + xy)

⇒ x³ - y³ = (x - y){ (x² + y²) + xy }

Substituting x² + y² = - xy

⇒ x³ - y³ = (x - y)( - xy + xy )

⇒ x³ - y³ = (x - y)(0)

⇒ x³ - y³ = 0

Identity used :-

➞ x³ - y³ = (x - y)(x² + y² + xy)

Some important identities :-

➞ (x + y)² = x² + y² + 2xy

➞ (x - y)² = x² + y² - 2xy

➞ (x + y)² = (x - y)² + 4xy

➞ (x - y)² = (x + y)² - 4xy

➞ (x + y)(x - y) = x² - y²

➞ (x + a)(x + b) = x² + (a + b)x + ab

➞ (x + y + z)² = x² + y² + z² + 2xy + yz + xz

➞ x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + y² - xy - yz - zx)