[tex]E( \sqrt{5} )= \frac{4-2\sqrt{5}}{\sqrt{5}+2} =\frac{(\sqrt{5}-2)(4-2\sqrt{5})}{(\sqrt{5}-2)(\sqrt{5}+2)} = \\ =\frac{4\sqrt{5}-10-8+4\sqrt{5}}{5-4}= \frac{8\sqrt{5}-18}{1}=2(4\sqrt{5}-9) \\ E( -\sqrt{5} )= \frac{4-2(-\sqrt{5})}{-\sqrt{5}+2} = \frac{4+2\sqrt{5}}{2-\sqrt{5}}= \\ =\frac{(2+\sqrt{5})(4+2\sqrt{5})}{(2+\sqrt{5})(2-\sqrt{5})} = \frac{8+4\sqrt{5}+4\sqrt{5}+10}{4-5}= \frac{8\sqrt{5}+18}{-1}= \\ =-( 8\sqrt{5}+18)=-2(4\sqrt{5}+9) [/tex]
[tex]2x^{2}-6x+18=2(\sqrt{5})^{2} -6\sqrt{5}+18= \\ =10-6\sqrt{5}+18=28-6 \sqrt{5} =2(14-3\sqrt{5}) \\ 2x^{2}-6x+18=2(-\sqrt{5})^{2} -6(-\sqrt{5})+18= \\ =10+6\sqrt{5}+18=28+6 \sqrt{5} =2(14+3\sqrt{5})[/tex]
