Question

determinati numerele x,y,z invers proportionale cu 3,6,9 stiind ca x+y+z = 42

Answer 1

Explicație pas cu pas:

$\frac{x}{ \frac{1}{3} } = \frac{y}{ \frac{1}{6} } = \frac{z}{ \frac{1}{9} } \iff 3x = 6y = 9z \\ \iff x = 2y = 3z = k$

$2y = k \implies y = \frac{k}{2} \\ 3z = k \implies z = \frac{k}{3}$

$x + y + z = k + \frac{k}{2} + \frac{k}{3} \\ 42 = \frac{6k + 3k + 2k}{6} \\ 11k = 252 \implies k = \frac{252}{11}$

$x = k \implies x = \frac{252}{11} \\ y = \frac{k}{2} \implies y = \frac{252}{22} = \frac{126}{11} \\ z = \frac{k}{3} \implies z = \frac{252}{33} = \frac{84}{11}$