[tex]\displaystyle Se ~ da: \\ \\ \frac{x}{a} =\frac{y}{b} =\frac{z}{c} \\ \\ a,~b,~c~~sunt~numere~prime \\ a\ \textless \ b\ \textless \ c \\ x \cdot y \cdot z = 139755 \\ \\ Se~cere: \\ A=x+y+z [/tex]
[tex]\displaystyle Rezolvare: \\ \\ \frac{x}{a} =\frac{y}{b} =\frac{z}{c} =k \\ =\ \textgreater \ ~~ x=ak,~~y = bk,~~z=ck ,unde ~a,~b,~c~~~sunt~numere~prime. \\ x \cdot y \cdot z = 139755 \\ ak \cdot bk \cdot ck = 139755 \\ a \cdot b \cdot c \cdot k^3 = 139755 \\ Descompunem~numarul~139755 \\
139755 = 3 \cdot 5 \cdot 7 \cdot 11^3 = a \cdot b \cdot c \cdot k^3 \\
=\ \textgreater \ a=3;~~~~~b=5;~~~~~ c=7;~~~~~ k=11 \\
x=ak = 3 \cdot 11 = \boxed{33} \\ y=bk = 5 \cdot 11 = \boxed{55} \\ z=ck = 7 \cdot 11 = \boxed{77} [/tex]
[tex]A=x+y+z =33+55+77=\boxed{165}[/tex]
