Question

Determine o valor das expressões:
a) (5 −√2)2
b) (3 +2)2 + (3 −√2)2
c) (1 −√3) · (1 +√2)

Answer 1

Resposta:

$a)\\ \\ (5-\sqrt{2} )^{2} =\\ \\ 5^{2} -2.5.\sqrt{2} +(\sqrt{2} )^{2} =\\ \\ 25-10\sqrt{2} +2=\\ \\ 27-10\sqrt{2} \\ \\ \\ b)\\ \\ (3+2)^{2} +(3-\sqrt{2} )^{2} =\\ \\ (3^{2} +2.3.2+2^{2} )+[3^{2} -2.3.\sqrt{2} +(\sqrt{2})^{2} ]=\\ \\ 9+12+4+9-6\sqrt{2} +2=\\ \\ 36-6\sqrt{2}$

$c)\\ \\ (1-\sqrt{3} ).(1+\sqrt{2} )=\\ \\ 1.1+1.\sqrt{2} -1.\sqrt{3} -\sqrt{3}. \sqrt{2} =\\ \\ 1+\sqrt{2} -\sqrt{3} -\sqrt{3.2} =\\ \\ 1+\sqrt{2} -\sqrt{3} -\sqrt{6}$