\[\begin{array}{l}
Tu\,\,\,de\,\,bai\,\,ta\,\,dat:\\
a = \frac{9}{4} + x;\,\,b = \frac{9}{4} + y;\,\,c = \frac{9}{4} + z;\,\,d = \frac{9}{4} + t\\
x + y + z + t = 0\\
\Rightarrow {a^2} + {b^2} + {c^2} + {d^2} = {(\frac{9}{4} + x)^2} + {(\frac{9}{4} + y)^2} + {(\frac{9}{4} + z)^2} + {(\frac{9}{4} + t)^2}\\
= {x^2} + \frac{9}{2}x + \frac{{81}}{{16}} + {y^2} + \frac{9}{2}y + \frac{{81}}{{16}} + {z^2} + \frac{9}{2}z + \frac{{81}}{{16}} + {t^2} + \frac{9}{2}t + \frac{{81}}{{16}}\\
= {x^2} + {y^2} + {z^2} + {t^2} + \frac{9}{2}(x + y + z + t) + \frac{{81}}{4}\\
= {x^2} + {y^2} + {z^2} + {t^2} + \frac{{81}}{4} \ge \frac{{81}}{4}\\
Vay\,\,\min ({a^2} + {b^2} + {c^2} + {d^2}) = \frac{{81}}{4} \Leftrightarrow x = y = z = t = 0 \Leftrightarrow a = b = c = d = \frac{9}{4}
\end{array}\]