Bonjour,
[tex]K = \left(\sqrt{5}+4\right)\left(3\sqrt{5}-2\right)\\ K = \sqrt 5 \times 3\sqrt 5 -2\times \sqrt 5 +4\times 3\sqrt 5 - 2\times 4\\ K = 3\times 5-2\sqrt 5+12\sqrt 5-8\\ K = 15+10\sqrt 5-8\\ K = 7+10\sqrt 5[/tex]
[tex]L = \left(3\sqrt 2+1\right)\left(3\sqrt 2-1\right)\\ L = \left(3\sqrt 2\right)^2-1^2\\ L = 3^2\times 2 -1= 18-1 = 17[/tex]
[tex]M = \left(7\sqrt 3 -2\right)\left(\sqrt 3 +3 \right)\\ M = 7\sqrt 3 \times \sqrt 3 + 7\sqrt 3 \times 3 - 2\sqrt 3-2\times 3\\ M = 7\times 3 +21\sqrt 3-2\sqrt 3-6\\ M = 21+19\sqrt 3-6\\ M = 15+19\sqrt 3[/tex]
[tex]N = \left(\sqrt{11}-1\right)\left(2\sqrt{11}-5\right)\\ N = \sqrt{11}\times 2\sqrt{11}-5\sqrt{11}-2\sqrt{11}+5\\ N = 2\times 11-7\sqrt{11}+5\\ N = 22+5-7\sqrt{11} = 27-7\sqrt{11}[/tex]
