Question

a/b=3,b/c=6 тогда (a^2+b^2+c^2)/ac

Answer 1

(a² + b² + c²)/ac = a/c + b²/ ac + c/a = ...
a/b = 3 = b / 2c;
2ac = b² ; 2a / c = (b/c)²; a/c = 18
... = 18 + 0.5 + 1 / 18 = 334 / 18 = 167 / 9

Answer 2

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

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

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