a,b,c

[mehmetutku]

$a \neq b$    ve   $a,b,c$    reel sayılar olmak üzere   $a^2(b+c)=b^2(a+c)=2013$     ise     $b(a^2+c^2)+ac(a+c)=?$

[erray]

 $\begin{array}{l} {a^{2} (b+c)=b^{2} (a+c)} \\ {a^{2} b-b^{2} a+a^{2} c-b^{2} c=0} \\ {\left(a-b\right)\left(ab+ac+bc\right)=0} \\ {ab+ac+bc=0} \\ {-b(a+c)=ac{\rm \; \; \; (*)}} \end{array}$      $\begin{array}{l} {b^{2} \left(a^{2} +c^{2} \right)+ac\left(a+c\right)} \\ {b^{2} \left(a^{2} +c^{2} \right)-b\left(a+c\right).\left(a+c\right)} \\ {-2abc} \end{array}$    $\begin{array}{l} {b^{2} (a+c)=2013} \\ {b.\left(-ac\right)=2013} \end{array}$ \[b^{2} \left(a^{2} +c^{2} \right)+ac\left(a+c\right)=4026\]