Question

Si: x+y=5; x³+ y³= 35

Calcula: xy

AYUDA PLISSS!!

Answer 1

Resolver.

Si
x + y = 5
x³ + y³ = 35

Hallar xy


Partes de:
(x + y)² = x² + 2xy + y²       Pero x + y = 5 reemplazas
 ( 5)² = x² + 2xy + y²
25 = x² + 2xy + y²
25 - 2xy = x² + y²     (1)

x³ + y³ = 35         Factorizas la suma de cubos
(x + y)(x² - xy + y²) =  35
5 (x² + y² - xy)      De 1 sustituyes
5(25 - 2xy - xy) = 35
5(25 - 3xy) = 35
125 - 15xy = 35
125 - 35 = 15xy
90 = 15xy
90/15 = xy
6 = xy

Respuesta.
xy = 6

Answer 2

(x+y)³ = 5³
x³ + 3x²y + 3xy² + y³ = 125
x³ + y³ + 3x²y + 3xy² = 125
  35 + 3xy(x+y) = 125  
      3xy(5) = 90
      3xy = 18
        xy = 6