Răspuns:
[tex]\boxed{\boxed{\bf \bigg(a;b;c \bigg) \in \bigg\{6;21;15 \bigg\} }}[/tex]
Explicație pas cu pas:
[tex]\bf \bigg(a\,;b\,;c \bigg) \; i.p. \; \bigg( \; \dfrac{1}{2}\, ;\, \dfrac{1}{7} \,;\dfrac{1}{5} \,\bigg)[/tex]
[tex]\bf a \cdot \dfrac{1}{2} = b\cdot \dfrac{1}{7} =c \cdot \dfrac{1}{5} =k[/tex]
[tex]\bf \implies a \cdot \dfrac{1}{2}=k \implies a=k: \dfrac{1}{2} = 2k[/tex]
[tex]\bf \implies b \cdot \dfrac{1}{7 } = k \implies b=k:\dfrac{1}{7} =7k[/tex]
[tex]\bf \implies c \cdot \dfrac{1}{5} =k \implies c=k:\dfrac{1}{5} =5k[/tex]
[tex]\bf \implies abc=1890 \implies a \cdot b \cdot c = 1890[/tex]
[tex]\bf \implies 2k \cdot 5k\cdot 7 k = 1890[/tex]
[tex]\bf \implies 70k^3 = 1890 \, | : 70 \implies k^3=27[/tex]
[tex]\bf \implies k= \sqrt[\bf 3]{\bf 27} \implies \boxed{\bf k=3}[/tex]
[tex]\bf a = 2k = 2 \cdot 3 \implies \boxed{\bf a = 6}[/tex]
[tex]\bf b=7k=7\cdot 3 \implies \boxed{\bf b=21}[/tex]
[tex]\bf c=5k = 5 \cdot 3 \implies \boxed{ \bf c = 15}[/tex]
Bafta! :)
#copaceibrainly
