Question

Resolva o sistema {

x + y = 7
loga x + loga y = loga 12

Answer 1

Resposta:

x = 4

y = 3

Explicação passo-a-passo:

x + y = 7

log$log_{a} x + log_{a} y = log_{a} 12$

.

$log_{a} x + log_{a} y = log_{a} 12$

$log_{a}(x*y) = log_{a} 12$

x*y = 12

.

x + y = 7

x = 7-y

.

Substituindo

x*y = 12

(7-y)*y=12

-y² + 7y - 12 = 0

.

y = $\frac{-7+\sqrt{7^{2}-4*-1*-12 } }{2*-1}$

y = $\frac{-7+\sqrt{49-48 } }{-2}$

y = $\frac{-7+\sqrt{1 } }{-2}$

y = $\frac{-7+1 }{-2}$

y = $\frac{-6 }{-2}$

y = 3

.

Portanto,

x + y = 7

x + 3 = 7

x = 7-3

x = 4