Question

Aflați inversul numărului rațional a=[ 0,1(6)-1]^7:(5 pe 6)^5

Va rog repede!!!mk

Answer 1

   
[tex]\displaystyle\\ a=[0,\!1(6)-1]^7:\Big(\frac{5}{6}\Big)^5=\\\\ =\left(\frac{16-1}{90}-1\right)^7:\Big(\frac{5}{6}\Big)^5=\\\\ =\left(\frac{15}{90}-1\right)^7:\Big(\frac{5}{6}\Big)^5=\\\\ =\left(\frac{1}{6}-1\right)^7:\Big(\frac{5}{6}\Big)^5=\\\\ =\left(\frac{1-6}{6}\right)^7:\Big(\frac{5}{6}\Big)^5=\\\\ =\left(\frac{-5}{6}\right)^7:\Big(\frac{5}{6}\Big)^5=\\\\ =-\left(\frac{5}{6}\right)^7:\Big(\frac{5}{6}\Big)^5= [/tex]

[tex]\displaystyle\\ =-\left(\frac{5}{6}\right)^{7-5}=-\left( \frac{5}{6}\right)^2=-\frac{5^2}{6^2}= -\frac{25}{36}\\\\ \Longrightarrow~~a = -\frac{25}{36}\\\\ \Longrightarrow~~ \boxed{\bf \frac{1}{a} = -\frac{36}{25}}~~~\texttt{(inversul lui a)}[/tex]