Question

Usando produtos notáveis, resolva: Qual é o valor de x - y, sabendo que o x + y = 6 e x² - y² = 54.


(A) 6

(B) 7

(C) 8

(D) 9

​

Answer 1

$\displaystyle \text x^2-\text y^2=54 \\\\ \text x+\text y=6\\\\ \text x-\text y =\ ? \\\\ \text{Fatorando o protudo not{\'a}vel}: \\\\ \text x^2-\text y^2=54 \\\\ (\text x-\text y)(\text x+\text y)=54 \\\\ (\text x-\text y).6=54 \\\\ \text x-\text y =\frac{54}{6}\\\\ \huge\boxed{\text x-\text y = 9\ }\checkmark$

letra D