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