Question

Daca a+b:2+c:2=22, a:2+b+c:2=24 si a:2+b:2+c=26 sa se afle a, b,c

Answer 1

a+b/2+c/2=22
a/2+b+c/2=24
a/2+b/2+c=26
Se elimina numtorii:
2a+b+c=44
a+2b+c=48
a+b+2c=52
Putem aplica substititia. Din prima ecuatie c=44-2a-b Inlocuim in celelalte doua:
a+2b+44-2a-b=48 ⇒ 44-a+b=48 ⇒b-a=4
a+b+2(44-2a-b)=52 ⇒ a+b+88-4a-2b=52 ⇒ 88-52=4a+2b-a-b ⇒ 36=3a+b

b-a=4  ⇒b=4+a
3a+b=36 inlocuim pe b:
3a+4+a=36 ⇒ 4a=32 ⇒ a=8
b=4+a ⇒ b=12
c=44-2a-b ⇒c=44-16-12 ⇒c=16
Proba:
a+b/2+c/2=8+12/2+16/2=8+6+8=22 OK
a/2+b+c/2=8/2+12+16/2=4+12+8=24  OK
a/2+b/2+c=8/2+12/2+16=4+6+16=26  OK