Question

Sa se rezolve ecuatiile [(3x-1)/2] = 5 .
[x + 1/2] = (2x+7) / 4
Parantezele patrate provin de la partea intreaga.

Answer 1

Răspuns:

Explicație pas cu pas:

[(3x+1)/2]=5

5≤(3x+1)/2<6

5*2≤3x+1<6*2

10≤3x+1<12

10-1≤3x<12-1

9≤3x<11

9/3≤x<11/3

3≤x<11/3

x∈[3,11/3)

----------------------

[x+1/2]=(2x+7)/4

[x+1/2]=k   k∈Z

(2x+7)/4=k

2x+7=4k

2x=4k-7

x=(4k-7)/2 (ii

Inlocuim x in relatia (ii

[(4k-7)/2+1/2]=k

[4k-7/2+1/2]=k

[4k/2-6/2]=k

[2k-3]=k

2k-3=k

2k-k=3

k=3 inlocuim k in relatia (ii

x=(4*3-7)/2

x=(12-7)/2

x=5/2