Question

Se x, y e z são números reais não nulos , tais que x + y + z = 17, x – y - z = 1 e x – y + z = 11 , então é CORRETO afirmar que o valor numérico da expressão x . y . z é igual a:

(A) 105 (B) 135 (C) 160 (D) 190

Answer 1

Olá



Resposta correta, Letra B) 135



Resolve o sistema para encontrar os valores de x, y, z.


Resolvendo pelo método do escalonamento


$\displaystyle\left\{\begin{array}{lll}\mathsf{x+y+z=17}~\\\mathsf{x-y+z=11}~\\\mathsf{x-y-z=1}\end{array}\right\\\\\\\\\mathsf{L2=L1-L2}\\\\\mathsf{L3=L1-L3}\\\\\\\\\left\{\begin{array}{lll}\mathsf{x+y+z=17}~\\\mathsf{\quad ~2y\quad ~~=6}~\\\mathsf{\quad ~2y+2z=16}\end{array}\right$


$\displaystyle \mathsf{L3=L3-L2}\\\\\\\\\left\{\begin{array}{lll}\mathsf{x+y+z=17}~\\\mathsf{\quad ~2y\quad ~~=6 \qquad\qquad\Longrightarrow \qquad ~\boxed{\mathsf{y=3}}}~\\\mathsf{\quad ~\quad~~2z=10\qquad\qquad\Longrightarrow \qquad \boxed{\mathsf{z=5}} }\end{array}\right$


Substituindo os valores de 'y' e 'z' na primeira equação


x + y + z = 17

x + 3 + 5 = 17

$\boxed{\mathsf{x=9}}$



$\mathsf{x\cdot y\cdot z= ?}\\\\\\\boxed{\mathsf{9\cdot 3\cdot 5~= ~135}}\qquad\qquad\qquad\Longrightarrow\qquad\text{Letra B)}$