[tex] {( \sqrt{5} - \frac{1}{2} )}^{2} + {( \frac{ \sqrt{2} }{2} + 1) }^{2} + ( \frac{1}{2} - \sqrt{5} )( \frac{1}{2} + \sqrt{5} )[/tex]
[tex] = 5 - \sqrt{5} + \frac{1}{4} + \frac{2}{4} + \sqrt{2} + 1 + \frac{1}{4} - 5[/tex]
[tex] = 2 + \sqrt{2} - \sqrt{5} [/tex]