Question

sean:

${x}^{3} + 3x {y}^{2} = 36$

$3 {x}^{2} y + {y}^{3} = 28$

Calcule el valor de:
$\frac{x + y}{x - y}$
​

Answer 1

Resolvemos:

(x + y)³ = x³ + 3 x² y + 3 x y² + y³ = (x³ + 3 x y²) + (3 x² y + y³)

(x + y)³ = 36 + 28 = 64; x + y = 4

(x - y)³ = x³ - 3 x² y + 3 x y² - y³ = (x³ + 3 x y²) - (3 x² y + y³)

(x - y)³ = 36 - 28 = 8; x - y = 2

Finalmente:

(x + y) / (x - y) = 4/2 = 2

Mateo.