Cho a, b, c là các số thực, theo thứ tự lập thành...

C

- Hướng dẫn giải

Ta có \(\left\{ {\begin{array}{*{20}{c}}{a + b + c = 26}\\{{a^2} + {b^2} + {c^2} = 364}\\{{b^2} = ac}\end{array}} \right.\). Từ đó ta có

\(\left\{ {\begin{array}{*{20}{c}}{{a^2} + ac + {c^2} = 364}\\{{{\left( {26 - a - c} \right)}^2} = ac}\end{array}} \right..\;\)

 Đặt \(\left\{ {\begin{array}{*{20}{c}}{S = a + c}\\{P = ac}\end{array}} \right.\) có hệ

\(\left\{ {\begin{array}{*{20}{c}}{{S^2} - P = 364}\\{{{(26 - S)}^2} = P}\end{array} \\\Leftrightarrow } \right.\left\{ {\begin{array}{*{20}{c}}{P = {{(26 - S)}^2}}\\{{S^2} - {{(26 - S)}^2} = 364}\end{array}} \right. \\\Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{P = {{\left( {26 - S} \right)}^2}}\\{S = 20}\end{array}} \right. \\\Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{S = 20}\\{P = 36}\end{array}} \right. \\\Rightarrow \left[ {\begin{array}{*{20}{c}}{\left\{ {\begin{array}{*{20}{c}}{a = 18}\\{c = 2}\end{array}} \right.}\\{\left\{ {\begin{array}{*{20}{c}}{a = 2}\\{c = 18}\end{array}} \right.}\end{array}} \right.\)

Vậy \({b^2} = ac = 36 \Rightarrow b = 6\)