Question

Determinați numerele raționale pozitive x,y,z care sunt invers proportionale cu numerele 2,3,4 iar 4x+5y-8z=240

Answer 1

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

4x+5y-8z=240

___________

x, y, z=?

_________

2x=3y=4z=k

2x=k => x=k/2

3y=k => y=k/3

4z=k => z=k/4

4k/2+5k/3-8k/4=240

2k+5k/3-2k=240

5k/3=240

5k=720/:5

k=144

=>x=144/2=72

y=144/3=48

z=144/4=36

➡ Kawaiimath

Answer 2

Răspuns:

2x=3y=4z=k

2x=k=>x=k/2

3y=k=>y=k/3

4z=k=>z=k/4

⁶⁾4k/2+⁴⁾5k/3-³⁾8k/4=¹²⁾240

24k+20k-24k=2880

20k=2880=>k=2880:20=>k=144

x=144:2=72

y=144:3=48

z=144:4=36