Explicație pas cu pas:
a)
[tex]( \sqrt{7} + \sqrt{3})( \sqrt{7} - \sqrt{3}) = {( \sqrt{7} )}^{2} - {( \sqrt{3} )}^{2} \\ = 7 - 3 = 4 \\ [/tex]
b)
[tex]{( \sqrt{5} - \sqrt{2})}^{2} + 2 \sqrt{2}(\sqrt{5} - \sqrt{2}) =\\= (\sqrt{5} - \sqrt{2})(\sqrt{5} - \sqrt{2} + 2 \sqrt{2}) \\ = {( \sqrt{5} )}^{2} - {( \sqrt{2} )}^{2} = 5 - 2 = 3[/tex]
c)
[tex]{(3 + 2 \sqrt{2})}^{2} - {(3 - \sqrt{8} )}^{2} = {(3 + 2 \sqrt{2})}^{2} - {(3 - 2 \sqrt{2} )}^{2} = \\ = (3 + 2 \sqrt{2} + 3 - 2 \sqrt{2})(3 + 2 \sqrt{2} - 3 + 2 \sqrt{2}) \\ = 6 \times 4 \sqrt{2} = 24 \sqrt{2} [/tex]
d)
[tex]{( \sqrt{2} - \sqrt{3})}^{2} - ( \sqrt{2} - \sqrt{3})(\sqrt{2} + \sqrt{3}) = \\ = ( \sqrt{2} - \sqrt{3})(\sqrt{2} - \sqrt{3} - \sqrt{2} - \sqrt{3}) \\ = ( \sqrt{2} - \sqrt{3})( - 2 \sqrt{3}) = - 2 \sqrt{6} + 6 \\ = 2(3 - \sqrt{6})[/tex]
