Answer
$x_1=1.618$ and $x_2=-0.618$
Work Step by Step
$e^{x^2-3}=e^{x-2}$
Using the One-to-One Property:
$x^2-3=x-2$
$x^2-x-1=0~$ ($a=1,~b=-1,~c=-1$):
$x=\frac{-(-1)±\sqrt {(-1)^2-4(1)(-1)}}{2(1)}=\frac{1±\sqrt 5}{2}$
$x_1=\frac{1+\sqrt 5}{2}\approx1.618$ and $x_2=\frac{1-\sqrt 5}{2}\approx-0.618$
