Răspuns:
a)
[tex]( \sqrt{2} )^{6} = {2}^{3} = 8[/tex]
[tex]( \frac{1}{2} )^{3} = \frac{1}{8} [/tex]
[tex]( \frac{ \sqrt{25} }{ \sqrt{2} } )^{6} = \frac{15625}{8} [/tex]
[tex]( \frac{5}{ \sqrt{2} } )^{4} = \frac{625}{4} [/tex]
[tex] \frac{15625}{8} \times \frac{4}{625} = \frac{25}{2} [/tex]
[tex] \sqrt{ \frac{16}{25} } = \frac{4}{5} [/tex]
[tex]8 \times \frac{1}{8} - \frac{25}{2} \times \frac{4}{5} = \\ 1 - 10 = \\ - 9 [/tex]
b)
[tex] \frac{1}{2 + \sqrt{3} } = \frac{2 - \sqrt{3} }{4 - 3} = 2 - \sqrt{3} [/tex]
[tex] \frac{2}{ \sqrt{3} - 1 } = \frac{2 \sqrt{3} - 2}{3 - 1} = \sqrt{3 } - 1[/tex]
Adunarea primei paranteze este 1
[tex] \frac{4}{3 \sqrt{2} + 4} = \frac{4(3 \sqrt{2} - 4)}{18 - 16} = 6 \sqrt{2} - 8[/tex]
[tex] \frac{3}{3 - 2 \sqrt{2} } = 9 + 6 \sqrt{2} [/tex]
Scăderea celei de-a doua paranteze este -17
Rezultatul final este (-17)
