Question

Se x = 2√3 - √2 e y = √3 - 2√2 calcule:

x•(x+y)

Answer 1

$x=2 \sqrt{3} - \sqrt{2} \\ y= \sqrt{3} -2 \sqrt{2} \\ \\x\cdot(x+y)\\ \\=(2\sqrt{3} - \sqrt{2})\cdot[(2\sqrt{3} - \sqrt{2})+(\sqrt{3} -2 \sqrt{2})]\\ \\=(2\sqrt{3} - \sqrt{2})\cdot[2\sqrt{3} - \sqrt{2}+\sqrt{3} -2 \sqrt{2}]\\ \\=(2\sqrt{3} - \sqrt{2})\cdot[3\sqrt{3} - 3\sqrt{2}]\\ \\=6\sqrt{9} - 6\sqrt{6}-3\sqrt{6} + 3\sqrt{4}\\ \\=6\cdot3 - 9\sqrt{6} + 3\cdot2\\ \\=18 - 9\sqrt{6} + 6\\ \\=24 - 9\sqrt{6} \\ \\=3\cdot(8 - 3\sqrt{6})$