Question

{x, y, z} i. p. {2,,3,4}

a)x+y-z=7
b) x+z-y=10
c) y+z -z=4

​

Answer 1

Răspuns:

Bună,

{x,y,z} i.p cu {2,3,4}

$\frac{x}{ \frac{1}{2} } = \frac{y}{ \frac{1}{3} } = \frac{z}{ \frac{1}{4} } = k \\ = > x = \frac{k}{2} \\ y = \frac{k}{3} \\ z = \frac{k}{4}$

$a)x + y - z = 7 \\ \frac{k}{2} + \frac{k}{3} - \frac{k}{4} = 7 | \times 12 \\ 6k + 4k - 3k = 84 \\ 7k = 84 \\ \blue{k = 12} \\ x = \frac{k}{2} = \frac{12}{2} = 6 \\ y = \frac{k}{3} = \frac{12}{3} = 4 \\ z = \frac{k}{4} = \frac{12}{4} = 3$

$b)x + z - y = 10 \\ \frac{k}{2} + \frac{k}{4} - \frac{k}{ 3} = 10 | \times 12 \\ 6k + 3k - 4k = 120 \\ 5k = 120 \\ \orange{ k = 24} \\ x = \frac{k}{2} = \frac{24}{2} = 12 \\ y = \frac{k}{3} = \frac{24}{3} = 8 \\ z = \frac{k}{4} = \frac{24}{4} = 6$

La c) dacă ai vrut să scrii :

y+z-z=4, atunci:

$\frac{k}{3} + \frac{k}{4} - \frac{k}{4} = 10 \\ \frac{k}{ 3} = 10 \\ = > \pink{k = 30} \\ x = \frac{k}{2} = \frac{30}{2} = 15 \\ y = \frac{k}{3} = \frac{30}{3} = 10 \\ z = \frac{k}{4} = \frac{30}{4} = 7.5$

Dar dacă ai vrut să scrii :

y+z-x=4 ,

$\frac{k}{3} + \frac{k}{4} - \frac{k}{2} = 4 |\times 12 \\ 4k + 3k - 6k = 48 \\ \green{ k = 48} \\ x = \frac{k}{2} = \frac{48}{2} = 24 \\ y = \frac{k}{3} = \frac{48}{3} = 16 \\ z = \frac{k}{4} = \frac{48}{4} = 12$

Sper că te-am ajutat.