Observăm că :
[tex]\it 41\pm12\sqrt5 = ( 6\pm\sqrt5)^2[/tex]
Ecuația devine:
[tex]\it c)\ \sqrt{(6-\sqrt5)^2} +\sqrt{(6+\sqrt5)^2} x =\sqrt{(6-\sqrt5)^2} x - \sqrt{(6-\sqrt5)^2} [/tex]
[tex]\it \Leftrightarrow 6-\sqrt5 +(6+\sqrt5)x =(6-\sqrt5)x - (6-\sqrt5)\Leftrightarrow [/tex]
[tex]\it \Leftrightarrow (6+\sqrt5-6+\sqrt5)x = -(6-\sqrt5) - (6-\sqrt5) \Leftrightarrow [/tex]
[tex]\it \Leftrightarrow 2\sqrt5 x = \sqrt5-6+\sqrt5-6 \Leftrightarrow 2\sqrt5 x = 2(\sqrt5-6)|_{:2} \Leftrightarrow [/tex]
[tex]\it \Leftrightarrow \sqrt5 x = \sqrt5-6 \Leftrightarrow x = \dfrac{^{\sqrt5)}\sqrt5-6} {\ \sqrt5} \Leftrightarrow x = \dfrac{5 - 6\sqrt5}{5}.[/tex]
