[tex]|x+2| +\sqrt{9+4\sqrt5} = 4+\sqrt5|y+3|,\qquad x, y \in \mathbb{Q}[/tex]
[tex]\sqrt{9+4\sqrt5} = \sqrt{(2+\sqrt5)^2} =2+\sqrt5[/tex]
Ecuatia se scrie:
[tex]|x+2| +2+\sqrt5} = 4+\sqrt5|y+3|[/tex]
O rearanjare a termenilor si efectuarea operatiilor imediate vor conduce la :
[tex]|x+2| -2 = \sqrt5(|y+3|-1)[/tex]
Aceasta ultima egalitate are loc intre numere rationale daca :
[tex]|x+2|-2 = 0 \ \ \ si \ \ \ |y+3| -1 = 0[/tex]
Din ultimele doua ecuatii, rezulta:
[tex]x=-4,\\\;\\ x=0\\\;\\
y=-4 \\\;\\ y = - 2[/tex]
