Question

a/b=3,b/c=6 тогда (a^2+b^2+c^2)/ac

Answer 1

$\frac{\big{a}}{\big{b}}*\frac{\big{b}}{\big{c}}=\frac{\big{a}}{\big{c}}\\\\3*6=\frac{\big{a}}{\big{c}}\:\:\:\:\:\:\:\Rightarrow\:\:\:\:\:\:\boldsymbol{\frac{\big{a}}{\big{c}}=18}}\\\\\\\\\frac{\big{a^2+b^2+c^2}}{\big{ac}}=\frac{\big{a^2}}{\big{ac}}+\frac{\big{b^2}}{\big{ac}}+\frac{\big{c^2}}{\big{ac}}=\frac{\big{a}}{\big{c}}+\frac{\big{b^2}}{\big{ac}}+\frac{\big{c}}{\big{a}}=\frac{\big{a}}{\big{c}}+\frac{\big{b}}{\big{a}}*\frac{\big{b}}{\big{c}}+\frac{\big{c}}{\big{a}}=$

$\\\\=18+\frac{\big{1}}{\big{3}}*6+\frac{\big1}{\big{18}}=20\:\frac{\big1}{\big{18}}$

$Otvet:\:\:20\:\frac{\big1}{\big{18}}$