Question

Un nr. nat. de 2 cifre este 2/9 din rasturnatul sau. Care este numarul? Va rog rezolvare completa!

Answer 1

[tex]\mathfrak{\overline{ab}= \frac{2}{9}*\overline{ba}~;a,b \neq 0} \\ \mathfrak{10a+b= \frac{2(10b+a)}{9} } \\ \mathfrak{10a+b= \frac{20b+2a}{9}} \\ \mathfrak{90a+9b=2a+20b} \\ \mathfrak{88a=11b} \\ \mathfrak{b=8a} \\ \mathfrak{Singura~varianta~este:} \\ \mathfrak{a=1~;b=8~pentru~ca~a,b \neq 0~si~daca~a=2 \longrightarrowb=16~si~nu~se~poate} \\ \boxed{\mathfrak{{\overline{ab}=18}}}[/tex]