Question

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Answer 1

Răspuns:

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

$b)(2 \sqrt{3} + \sqrt{24} )(2 \sqrt{6} - \sqrt{12} ) = (2 \sqrt{3} + \sqrt{4 \times 6} )(2 \sqrt{6} - \sqrt{3 \times 4} ) = \\ = (2 \sqrt{3} + 2 \sqrt{6} )(2 \sqrt{6} - 2 \sqrt{3} ) = (2 \sqrt{6} + 2 \sqrt{3} )(2 \sqrt{6} - 2 \sqrt{3} ) = \\ = ( {2 \sqrt{6} })^{2} - ( {2 \sqrt{3} })^{2} = 2 \sqrt{6} \times 2 \sqrt{6} - 2 \sqrt{3} \times 2 \sqrt{3} = 4 \times 6 - 4 \times 3 = 24 - 12 = 12$

$c)( \sqrt{2} - \sqrt{3} )( \sqrt{3} + \sqrt{2} ) - ( \sqrt{5} + 2 \sqrt{2} )(2 \sqrt{2} - \sqrt{5} ) = \\ = ( \sqrt{2} - \sqrt{3} )( \sqrt{2} + \sqrt{3} ) - ( {2 \sqrt{2} + \sqrt{5})(2 \sqrt{2} - \sqrt{5}) } = \\ = ( { \sqrt{2} })^{2} - ( { \sqrt{3} })^{2} - (( {2 \sqrt{2} })^{2} - ( { \sqrt{5} })^{2} ) = \\ = 2 - 3 - (2 \sqrt{2} \times 2 \sqrt{2} - 5) = \\ = - 1 - (4 \times 2 - 5) = - 1 - (8 - 5) = - 1 - 3 = - 4$

$d)(2 - \sqrt{3} )( \sqrt{3} + 2) + (3 + \sqrt{2} )( \sqrt{2} - 3) = \\ = (2 - \sqrt{3} )(2 + \sqrt{3} ) + ( \sqrt{2} + 3)( \sqrt{2} - 3) = \\ = {2}^{2} - ( { \sqrt{3} })^{2} + ( { \sqrt{2} })^{2} - {3}^{2} = \\ = 4 - \sqrt{3} \times \sqrt{3} + \sqrt{2} \times \sqrt{2} - 9 = 4 - 3 + 2 - 9 = 1 + 2 - 9 = 3 - 9 = - 6$