Question

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Answer 1

Răspuns:

$a)( \sqrt{7} + \sqrt{ 3} )( \sqrt{7} - \sqrt{3} ) = ( { \sqrt{7)} }^{2} - ( \sqrt{3} ) ^{2} = 7 - 3 = 4$

$b) {( \sqrt{5} - \sqrt{2}) }^{2} + 2 \sqrt{2} ( \sqrt{5} - \sqrt{2} ) = 5 - 2 \times \sqrt{5} \times \sqrt{2} + 2 + 2 \sqrt{2} \times \sqrt{5} + 2 \sqrt{2} \times ( - \sqrt{2} ) = \\ = 7 - 2 \sqrt{10} + 2 \sqrt{10} - 4 = 7 - 4 = 3$

$c)( {3 + 2 \sqrt{2} })^{2} - ( {3 - \sqrt{8} })^{2} = ( {3 + 2 \sqrt{2} })^{2} - ( {3 - 2 \sqrt{2} })^{2} = (9 + 2 \times 3 \times 2 \sqrt{2} + 8) - (9 - 2 \times 3 \times 2 \sqrt{2} + 8) = \\ = 17 + 12 \sqrt{2} - (17 - 12 \sqrt{2}) = 17 + 12 \sqrt{2} - 17 - 12 \sqrt{2} = 0$

$d) {( \sqrt{2} - \sqrt{3}) }^{2} - ( \sqrt{2} - \sqrt{3} )( \sqrt{2} + \sqrt{3} ) = \\ = 2 - 2 \times \sqrt{2} \times \sqrt{3} + 3 - (2 - 3) = \\ = 2 - 2 \sqrt{6} + 3 - ( - 1) \\ = - 2 \sqrt{6} + 5 + 1 = - 2 \sqrt{6} + 6$