Question

Se x + y =9 e x - y =5, então o valor de x² - y² é igual a:
A) 14
B) 28
C) 45
D) 56

Estou precisando urgente de ajuda!!

Answer 1

Alternativa C: $45$

$x^2 - y^2\ Diferenca\ de\ dois\ quadrados.\\\\(x + y).(x - y)\\\\9 . 5\\\\45$

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Answer 2

$\Large\boxed{\begin{array}{l}\underline{\rm Fatorac_{\!\!,}\tilde ao~da~diferenc_{\!\!,}a}\\\underline{\rm de~dois~quadrados}\\\huge\boxed{\boxed{\boxed{\boxed{\sf a^2-b^2=(a-b)\cdot (a+b)}}}} \end{array}}$

$\boxed{\begin{array}{l}\tt dados\begin{cases}\sf x-y=5\\\sf x+y=9\end{cases}\\\sf x^2-y^2=(x-y)\cdot(x+y)\\\sf x^2-y^2=5\cdot9\\\sf x^2-y^2=45\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~C}}}} \end{array}}$