解:將方程?$t^2+2\sqrt {3}t = 4$?化為一般形式
?$t^2+2\sqrt {3}t - 4 = 0,$?
其中?$a = 1,$??$b = 2\sqrt {3},$??$c = -4。$?
?$ $?先計(jì)算判別式?$?=b^2-4ac$?
?$=(2\sqrt {3})^2-4×1×(-4)$?
?$=12 + 16 $?
?$= 28。$?
?$ $?再根據(jù)求根公式?$t=\frac {-b\pm \sqrt {b^2-4ac}}{2a}$?可得:
?$ t=\frac {-2\sqrt {3}\pm \sqrt {28}}{2}=\frac {-2\sqrt {3}\pm 2\sqrt {7}}{2}=-\sqrt {3}\pm \sqrt {7},$?
?$ $?所以?$t_{1}=-\sqrt {3}+\sqrt {7},$??$t_{2}=-\sqrt {3}-\sqrt {7}。$?