Question

determinați nr. a,b,c stiind ca sunt i.p cu 0, (3); 0,5; 0,25 si ca 6a+2b-5c=50

Answer 1

[tex]\{a,b,c\}i.p.\{0,(3);\ 0,5;\ 0,25\}\Rightarrow \dfrac{a}{\dfrac{1}{\frac{1}{3}}}= \dfrac{b}{\dfrac{1}{\frac{1}{2}}}= \dfrac{c}{\dfrac{1}{\frac{1}{4}}}\Rightarrow \dfrac{a}{3}=\dfrac{b}{2}=\dfrac{c}{4}=k\Rightarrow\\ \Rightarrow a=3k,b=2k,c=4k\\ 6a+2b-5c=50\\ 18k+4k-20k=50\\ 2k=50\Rightarrow \boxed{k=25}\\ a=3k\Rightarrow \boxed{a=75}\\ b=2k\Rightarrow \boxed{b=50}\\ c=4k\Rightarrow \boxed{c=100}\\ R\text{Numerele cautate sunt 75,50 si 100.}[/tex]