Question

AYUDAAAAA PORFIS !!! el la 14

Answer 1

1) Veamos el dato

             $x+y=\sqrt{5xy}\\ \\ (x+y)^2=5xy\\ \\ x^2+2xy+y^2=5xy\\ \\ \dfrac{x^2+2xy+y^2}{xy}=5\\ \\ \\ \dfrac{x}{y}+\dfrac{y}{x}=3$

2) 

$E=\left(\dfrac{x}{y}+1\right)^3+\left(\dfrac{y}{x}+1\right)^3\\ \\ \\ E=\left(\dfrac{x}{y}+\dfrac{y}{x}+2\right)\left(\left(\dfrac{x}{y}+1\right)^2-\left(\dfrac{x}{y}+1\right)\left(\dfrac{y}{x}+1\right)+\left(\dfrac{y}{x}+1\right)^2\right)\\ \\ \\ E=(3+2)\left\{\left[\left(\dfrac{x}{y}+1\right)+\left(\dfrac{y}{x}+1\right)\right]^2-3\left(\dfrac{x}{y}+1\right)\left(\dfrac{y}{x}+1\right)\right\}$


$E=5\left[5^2-3\left(\dfrac{x}{y}+1\right)\left(\dfrac{y}{x}+1\right)\right]\\ \\ \\ E=5\left[25-3\left(2+\dfrac{x}{y}+\dfrac{y}{x}\right)\right]\\ \\ \\ E=5(25-3\cdot5)\\ \\ \boxed{E=50}$