Question

Determinati numerele rationale pozitive x,y si z care sunt invers proportionale cu numerele 6,8 si 16 iar 3x+5y-11z=630

Answer 1

x/1/6=y/1/8=z/1/16=k

6x=8y=16z=k

x=k/6;

y=k/8;

z=k/16;

3x+5y-11z=630

3/6k+5/8k-11/16k=630

24k+30k-33k=30240

21k=30240

k=30240/21

k=1440;

x=1440/6⇒x=240;

y=1440/8⇒y=180;

z=1440/16⇒z=90.

Verificam:

3x+5y-11z=630

3*240+5*180-11*90=630⇒630=630.

Bafta!

Answer 2

{ X, Y, Z } i.p { 6, 8, 16 }

X × 6 = Y × 8 = Z × 16 = k

X × 6 = k ⇒ X = k/6 ; Y × 8 = k ⇒ Y = k/8 ; Z × 18 = k ⇒ Z = k/`16

3X + 5Y - 11Z = 630

3×K/6+5×K/8-11×K/16= 630

K =1440

X = k/6=1440/6=240

Y = 1440/8 =180

Z = k/`16 = 1440/16=90

VERIFICARE

3x+5y-11z=630

3×240+5×180-11×90=630

630=630