Question

1+ Aplicando, a regra dos produtos notáveis calcule A (√5 + √7²= B (2√3+√2² = C (2+√2)² = D 3√5+√7²= ​

Answer 1

Resposta:

$a) \: ( \sqrt{5} + \sqrt{7} ) {}^{2} \\ \ { \sqrt{5} }^{2} + 2 \sqrt{5} \sqrt{7} + { \sqrt{7} }^{2} \\ 5 + 2 \sqrt{35} + 7 \\ 12 + 2 \sqrt{35}$

$b) \: {(2 \sqrt{3} + \sqrt{2} )}^{2} \\ {(2 \sqrt{3} )}^{2} + 2 \times 2 \sqrt{3} \sqrt{2} + { \sqrt{2} }^{2} \\ 4 \times 3 + 4 \sqrt{6} + 2 \\ 12 + 4 \sqrt{6} + 2 \\ = 14 + 4 \sqrt{6}$

$c) \: {(2 + \sqrt{2} )}^{2} \\ {2}^{2} + 2 \times 2 \sqrt{2} + { \sqrt{2} }^{2} \\ 4 + 4 \sqrt{2} + 2 \\ = 6 + 4 \sqrt{2}$

$d) \: {(3 \sqrt{5} + \sqrt{7}) }^{2} \\ {(3 \sqrt{5} )}^{2} + 2 \times 3 \sqrt{5} + { \sqrt{7} }^{2} \\ 9 \times 5 + 6 \sqrt{35} + 7 \\ 45 + 6 \sqrt{35} + 7 \\ = 52 + 6 \sqrt{35}$