\[\boxed{\mathbf{1139}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]
\[x^{2} + bx - 23 = 0\]
\[x_{1} = {- x}_{2}\text{\ \ \ \ }\]
\[x_{1} + x_{2} = - b\]
\[- x_{2} + x_{2} = - b\]
\[b = 0\]
\[x^{2} - 23 = 0\]
\[x^{2} = 23\]
\[x = \pm \sqrt{23}\]
\[Ответ:x = \pm \sqrt{23}\ при\ b = 0.\]