Question

$l = c + 1 \\ \frac{1}{l} + \frac{1}{c} = \frac{7}{12}$
Qual o valor de L e de C??​

Answer 1

1)L = C + 1

2)1/L + 1/C = 7/12

C/LC + L/LC = 7/12

(L + C)/LC = 7/12

12(L + C) = 7LC

12(C + 1 + C) = 7.(C + 1).C

12C + 12 + 12C = 7C² + 7C

24C + 12 = 7C² + 7C

7C² + 7C - 24C - 12 =0

7C² - 17C - 12 = 0

Δ = 289 + 336 = 625

√Δ = ± 25

C = 17 ± 25 / 14

C' = 3

C'' = - 4/7

Para C = 3, fica:

L = C + 1

L = 3 + 1

L = 4

Para C = - 4/7

L =  C + 1

L = 1 - 4/7

L = 7/7 - 4/7

L = 3/7

Respostas:

1) C = 3 e L = 4

2) C = - 4/7 e L = 3/7