[tex]\bf{a) \: ( \sqrt{3} + 1) {}^{2} - \sqrt{3} (4 + 3 \sqrt{3}) }[/tex]
[tex]\bf{3 + 2 \sqrt{3} + 1 - 4 \sqrt{3} - 9 = \boxed{\bf - 5 - 2 \sqrt{3} }}[/tex]
[tex]\bf{b) \: ( \sqrt{5} - 3) {}^{2} + 3 \sqrt{5}(2 - \sqrt{5} ) }[/tex]
[tex]\bf{5 - 6 \sqrt{5} + 9 - 6 \sqrt{5} - 15 = \boxed{\bf - 1 - 12 \sqrt{5} }}[/tex]
[tex]\bf{c) \: 2( \sqrt{2} + 3) {}^{2} - 4 \sqrt{2} (3 - \sqrt{2} ) }[/tex]
[tex]\bf{2(2 + 6 \sqrt{2} + 9) - 12 \sqrt{2} + 8}[/tex]
[tex]\bf{2(11 + 6 \sqrt{2}) - 12 \sqrt{2} + 8 }[/tex]
[tex]\bf{22 + 12 \sqrt{2} - 12 \sqrt{2} + 8 = \boxed{\bf 30}}[/tex]
[tex]\bf{d) \: 3( \sqrt{3} - 1) {}^{2} - \sqrt{3} ( \sqrt{3} - 6) - ( \sqrt{11} - \sqrt{2} )( \sqrt{11} + \sqrt{2} )}[/tex]
[tex]\bf{3(3 - 2 \sqrt{3} + 1) - 3 + 6 \sqrt{3} - (11 - 2) }[/tex]
[tex]\bf{3(4 - 2 \sqrt{3} ) - 3 + 6 \sqrt{3} - 9}[/tex]
[tex]\bf{12 - 6 \sqrt{3} - 3 + 6 \sqrt{3} - 9 \: = \boxed{\bf 0}}[/tex]
[tex]\bf{e) \: (2 \sqrt{5} + 1) {}^{2} + ( \sqrt{7} + \sqrt{2} )( \sqrt{7} - \sqrt{2} ) - \sqrt{80} }[/tex]
[tex]\bf{20 + 4 \sqrt{5} + 1 + ( \sqrt{7} + \sqrt{2} )( \sqrt{7} - \sqrt{2} ) - 4 \sqrt{5} }[/tex]
[tex]\bf{20 + 1 + 7 - 2 = 21 + 5 =\boxed{\bf 26}}[/tex]
[tex]\bf{f) \: (5 \sqrt{3} - 7)(5 \sqrt{3} + 7) - (3 \sqrt{3} - 1) {}^{2} - \sqrt{108} }[/tex]
[tex]\bf{(5 \sqrt{3} - 7)(5 \sqrt{3} + 7) - (27 - 6 \sqrt{3} + 1) - 6 \sqrt{3} }[/tex]
[tex]\bf{(5 \sqrt{3} - 7)(5 \sqrt{3} + 7) - (28 - 6 \sqrt{3} ) - 6 \sqrt{3} }[/tex]
[tex]\bf{(5 \sqrt{3} - 7)(5 \sqrt{3} + 7) - 28 + 6 \sqrt{3} - 6 \sqrt{3} }[/tex]
[tex]\bf{25 \times 3 - 49 - 28}[/tex]
[tex]\bf{75 - 49 - 28 = 75 - 77 =\boxed{\bf - 2}}[/tex]
Gliseaza spre dreapata pentru a vedea rezolvarea completa
Bafta ! :)
