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Determinati numerele naturale a, b, c, stiind ca indeplinesc simultan conditiile:
a+2b=47, b+2c=55 , c+2a=45

Răspuns :

Icecon2005
a+2b=47, b+2c=55 , c+2a=45
a=47-2b
c+2a=45
c+2(47-2b)=45
c+94-4b=45
c-4b=45-94
-3b=-49
b=49/3
a=47-2b=47-94/3=(47×3-94)/3
a= 47/3
c=45-2a=[45×3-(2×47)]/3=(135-94)/3=41/3
c=41/3
Verificare
c+2a=45
41/3+(2×47)/3=45
(41+94)/3=45
135/3=45
45=45

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