Question

SUMA A 3 NUMERE ESTE 120 . AFLATI NUMERELE STIIND CA ELE SUNT DIRECT PROPORTIONALE CU 2 SI 5 SI PRODUSUL LOR ESTE 360

Answer 1

a+b+c=120;
⇒a/2=b/5=k;
⇒a=2k;
⇒b=5k;
⇒a·b·c=360;
⇒2·k·5·k·c=360
⇒10·k²·c=360
⇒k²·c=36⇒k²∈[1,4,9,36];⇒1=1²;⇒4=2²;⇒9=3²;⇒36=6²;
⇒k∈[1,2,3,6]⇒c∈[36,9,4,1];⇒patru variante de raspuns;
⇒c=36⇒a+b=84⇒7k=84⇒k=12;
⇒a=24⇒b=60;
⇒24·60·36≠360⇒fals;
⇒c=9⇒a+b=111⇒7k=111⇒k∉N⇔fals;
⇒c=4⇒a+b=116⇒7k=116⇒k∉N⇔fals;
⇒c=4⇒a+b=119⇒7k=119⇒k=17;
⇒a=34;⇒b=85;
⇒34·85·17≠360⇒fals⇒problema gresita;