Question

Determinati numerele naturale a,b si c din: a:2+b+c:2=40, a+b:2+c:2=38, iar a:2+b:2+C=42

Answer 1

a+b/2+c/2=38=> 2a+b+c=38*2=>2(80-2b-c)+b+c=160-4b-2c+b+c=160-3b-c
a/2+b+c/2=40 => a+2b+c=40*2=>a=80-2b-c
a/2+b/2+c=42=> a+b+2c=42*2=>80-2b-c+b+2c=84=>-b+c=4
-3b-c=160
-b+c=4
-4b/=164 b=-41
-b+c=4 =>-(-41)+c=4 41+c=4  c=-41+4 c=-37
a=80-2(-41)-(-37)
a=80+82+37 a=199
verificare
a/2+b+c/2=40 => 199/2-41-37/2=80   199-82-37=80 deci verifica relatia