Question

If X upon Y + Y upon x is equal to -1 (x,y≠ 0) the value of x cube minus y cube is

Answer 1

Answer:

x³ - y³ = 0.

Step-by-step explanation:

$\frac{x}{y} +\frac{y}{x} = -1$

$\frac{x^2+y^2}{xy}=-1$

x² + y² = -xy

x² + y² + xy = 0.

Required x³ - y³

We know that a³ + b³ = (a + b)(a² + b² - ab)

Therefore x³ - y³ = (x+(-y))(x²+(-y)²-x(-y))

x³-y³ = (x - y)(x² + y² + xy) (From above x² + y² + xy = 0)

∴ x³ - y³ = 0.

Answer 2

Step-by-step explanation:

Answer:

x³ - y³ = 0.

Step-by-step explanation:

\frac{x}{y} +\frac{y}{x} = -1

y

x

+

x

y

=−1

\frac{x^2+y^2}{xy}=-1

xy

x

2

+y

2

=−1

x² + y² = -x

x² + y² + xy = 0.

Required x³ - y³

We know that a³ + b³ = (a + b)(a² + b² - ab)

Therefore x³ - y³ = (x+(-y))(x²+(-y)²-x(-y))

x³-y³ = (x - y)(x² + y² + xy) (From above x² + y² + xy = 0)

∴ x³ - y³ = 0.