Question

Fie a,b,c numre naturale distincte. Daca sunt indeplinite conditiile 2a+3b=c+13 si 3a+2b=17-c, cate valori distincte poate lua c?

Answer 1

2a+3b=c+13

3a+2b=17-c

__________+

5a+5b=30

5(a+b)=30 |:5

a+b=6 |·2

2a+2b=12

2a+3b=c+13

2a+2b=12

__________-

b=c+1

3a+2b=17-c

2a+2b=12

_________-

a=5-c

Dar a+b=(5-c)+(c+1)

a+b=5-c+c+1

a+b=6 (Asevarat)

c poate avea ORICE valoare

c€|N