Răspuns:
[tex]\red{\Large \bf a = 48~primul ~ numar}[/tex]
[tex]\pink{\Large\bf b = 72~al ~doilea ~numar}[/tex]
[tex]\green{\Large\bf c = 96~~al ~treilea~numar}[/tex]
Explicație pas cu pas:
[tex]\red{\large\boxed{\bf Media_{aritmetica}=\dfrac{a_{1}+a_{2}+a_{3}+a_{4}+....+a_{n}}{n}}}[/tex]
Notam cu:
a - primul număr
b - al doilea număr
c - al treilea număr
[tex]\left.\begin{matrix}\large\bf M_{a}=\dfrac{a+b+c}{3}\\\\ \large\bf M_{a}=72\end{matrix}\right\}\implies \large\bf \dfrac{a+b+c}{3}= 72 \implies \boxed{\bf a+b+c = 216}
[/tex][tex]\large\bf a+\dfrac{3a}{2} +2a= 126~~~\bigg|\cdot 2[/tex]
[tex]\it~~[/tex]
[tex]\large \bf b = a + 50\% \cdot a \implies b = a + \dfrac{\not50a}{\not100} \implies \boxed{\bf b = \dfrac{3a}{2} }[/tex]
[tex]\it~~~[/tex]
[tex]\left.\begin{matrix} \large\bf c=\dfrac{1}{3} \cdot b +b\\\\\large \bf b = \dfrac{3a}{2} \end{matrix}\right\}\implies\large \bf c =\dfrac{1}{\not3}\cdot\dfrac{\not3a}{2}+\dfrac{3a}{2}\implies c = \dfrac{a}{2}+\dfrac{3a}{2}\implies [/tex]
[tex]\large \bf \implies c =\dfrac{4a}{2}\implies c = \dfrac{\not4a}{\not2}\implies \boxed{\bf c= 2a }[/tex]
Înlocuim in suma si vom avea:
[tex]\large\bf a+\dfrac{3a}{2} +2a= 216~~~\bigg|\cdot 2[/tex]
[tex]\large\bf 2a+3a +4a= 432[/tex]
[tex]\large\bf 9a= 432~~~\bigg|:9[/tex]
[tex]\red{\Large\boxed{\bf a = 48}}[/tex]
[tex]\large \bf b = \dfrac{3\cdot 48}{2} \implies b = 3\cdot 24 \implies \pink{\Large\boxed{\bf b = 72}}[/tex]
[tex]\large \bf c = 2\cdot 48 \implies \green{\Large\boxed{\bf c = 96}}[/tex]
PS: Daca esti pe telefon te rog sa glisezi spre stânga pentru a vedea rezolvarea
#copaceibrainly
