Răspuns:
[tex]a = \sqrt{( - { \sqrt{3} )}^{2} } - ( - \frac{2}{3} ) ^{ - 2} + \frac{9}{4} - 2 \sqrt{3} \\ a = \sqrt{3} - ( - \frac{3}{2} ) ^{2} + \frac{9}{4} - 2 \sqrt{3} \\ a = \sqrt{3} - ( + \frac{9}{4} ) + \frac{9}{4} - 2 \sqrt{3} \\ a = \sqrt{3} - \frac{9}{4} + \frac{9}{4} - 2 \sqrt{3} \\ a = \sqrt{3} - 2 \sqrt{3} \\ a = - \sqrt{3} [/tex]
[tex]a)a = - \sqrt{3} \\ {a}^{2} = ( - { \sqrt{3} })^{2} = - \sqrt{3} \times ( - \sqrt{3} ) = 3 \\ {a}^{3} = ( - \sqrt{3} ) ^{3} = - \sqrt{3} \times ( - \sqrt{3} ) \times ( - \sqrt{3} ) = 3 \times ( - \sqrt{3} ) = - 3 \sqrt{3} \\ {a}^{4} = {a}^{2} \times {a}^{2} = 3 \times 3 = 9 \\ {a}^{5} = {a}^{3} \times {a}^{2} = - 3 \sqrt{3} \times 3 = - 9 \sqrt{3} \\ {a}^{6} = {a}^{4} \times {a}^{2} = 9 \times 3 = 27 \\ {a}^{7} = {a}^{5} \times {a}^{2} = - 9 \sqrt{3} \times 3 = - 27 \sqrt{3} \\ {a}^{8} = {a}^{4} \times {a}^{4} = 9 \times 9 = 81 \\ {a}^{9} = {a}^{5} \times {a}^{4} = - 9 \sqrt{3} \times 9 = - 81 \sqrt{3} \\ {a}^{10} = {a}^{8} \times {a}^{2} = 81 \times 3 = 243[/tex]
[tex]b) {a}^{ - 2} = \frac{1}{ {a}^{2} } = \frac{1}{3} \\ {a}^{ - 4} = \frac{1}{ {a}^{4} } = \frac{1}{9} \\ {a}^{ - 6} = \frac{1}{ {a}^{6} } = \frac{1}{27} \\ {a}^{ - 8} = \frac{1}{ {a}^{8} } = \frac{1}{81} \\ {a}^{ - 2} + {a}^{ - 4} + {a}^{ - 6} + {a}^{ - 8} = \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81} = \frac{1 \times 27}{81} + \frac{1 \times 9}{81} + \frac{1 \times 3}{81} + \frac{1}{81} = \frac{27 + 9 + 3 + 1}{81} = \frac{40}{81} [/tex]
40/81 €Q
