Prin formula radicalilor dubli
[tex] \sqrt{3+ \sqrt{5} } [/tex]
3=a
5=b
c=[tex] \sqrt{a^{2}-b } [/tex] = [tex] \sqrt{9-5} [/tex]=√4=2
[tex] \sqrt{3+ \sqrt{5} } [/tex] = [tex] \sqrt{ \frac{a+c}{2} } + \sqrt{ \frac{a-c}{2} } [/tex]=[tex] \sqrt{ \frac{3+2}{2} } + \sqrt{ \frac{3-2}{2} } = \sqrt{ \frac{5}{2} } + \sqrt{ \frac{1}{2} } , iar \sqrt{3- \sqrt{5} } = \sqrt{ \frac{5}{2} } - \sqrt{ \frac{1}{2} } [/tex][tex]x= \sqrt{ \frac{5}{2} } + \sqrt{ \frac{1}{2} } + \sqrt{ \frac{5}{2} } - \sqrt{ \frac{1}{2} }= 2 \sqrt{ \frac{5}{2} } [/tex]
[tex] \sqrt{10} - 2 \sqrt{ \frac{5}{2} } -1 =\sqrt{10} -2 \sqrt{ \frac{25}{100} } -1 =\sqrt{10} - 2 *\frac{5}{10} -1 [/tex][tex]= \sqrt{10} - \frac{10}{10} -1 = \sqrt{10} - 1 -1 = \sqrt{10} -2 [/tex]
