Question

x+y=4 calcular E= x ^3+y ^3-64/x ^2+y ^2-16

Answer 1

Respuesta:

6

Explicación paso a paso:

x + y = 4

Entonces:

(x + y)² = x² + 2xy + y²

(4)² = x² + y² + 2xy

16 - 2xy = x² + y²

...

x³ + y³ = (x + y)(x² - xy + y²)

x³ + y³ = (4)(x² + y² - xy)

x³ + y³ = (4)(16 - 2xy - xy)

x³ + y³ = 4(16 - 3xy)

x³ + y³ = 64 - 12xy

Entonces:

E = (x³ + y³ - 64) ÷ (x² + y² - 16)

E = (64 - 12xy - 64) ÷ (16 - 2xy - 16)

E = (-12xy) ÷ (-2xy)

E = $\frac{-12xy}{-2xy}$

E = $\frac{12xy}{2xy}$

E = $\frac{12}{2}$

E = 6