Question

2. (IFCE) Sejam x, y ER, com x+y=-16 e xy = 64. O valor da expressão x/y + y/z é:

a) -2
b) -1
c) 0
d) 1
e) 2​

Answer 1

$\Large\boxed{\begin{array}{l}\sf (IFCE)~Sejam~x,y\in\mathbb{R},com~x+y=-16~e~xy=64.\\\sf O\,valor\,da\,express\tilde ao~\dfrac{x}{y}+\dfrac{y}{x}~\acute e:\\\sf a)-2\\\sf b)-1\\\sf c)0\\\sf d)1\\\sf e)2\checkmark\end{array}}$

$\huge\boxed{\begin{array}{l}\sf (x+y)=-16~~xy=64\\\sf x^2+y^2=(x+y)^2-2xy\\\sf x^2+y^2= (-16)^2-2\cdot64\\\sf x^2+y^2=256-128\\\sf x^2+y^2=128\\\sf\dfrac{x}{y}+\dfrac{y}{x}=\dfrac{x^2+y^2}{xy}\\\\\sf\dfrac{x}{y}+\dfrac{y}{x}=\dfrac{128}{64}\\\\\boxed{\boxed{\boxed{\boxed{\sf\dfrac{x}{y}+\dfrac{y}{x}=2}}}}\end{array}}$