Answer:
x³ - y³ = 0
Step-by-step explanation:
Given : [tex]\frac{x}{y}+\frac{y}{x}=-1[/tex]
To Find : value of (x³ - y³)
Since, [tex]\frac{x}{y}+\frac{y}{x}=-1[/tex]
[tex]\frac{x^2+y^2}{xy}=-1[/tex]
x² + y² = -xy
x² + y² + xy = 0 -----(1)
Since, x³ - y³ = (x - y)(x² + xy + y²) [From the formula, (a³ - b³) = (a -b)(a²+ b² + ab)
= (x - y)(0) {From equation (1)]
= 0
Therefore, value of x³ - y³ = 0 will be the answer.
