Question

DETERMINE O VALOR DAS EXPRESSOES

A) $\frac{2}{5} - \frac{1}{6} + \frac{1}{2}$


B) ( 4 - $\sqrt{3}$) ²

C) ( 2 + $\sqrt{2}$) ² . ( 2 - $\sqrt{2}$ )²

Answer 1

$a) \\ \\ \dfrac{2}{5} - \dfrac{1}{6} + \dfrac{1}{2}$

MMC de 5, 6, 2  = 30

$\dfrac{2}{5} - \dfrac{1}{6} + \dfrac{1}{2} \\ \\ \\ \dfrac{12 - 5 + 15}{30} \\ \\ \\ \dfrac{22}{30} \ => \ \dfrac{11}{15}$

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$b) \\ \\ (4 - \sqrt{3})^2 \\ \\ \\ (4 - \sqrt{3}) * (4 - \sqrt{3}) \\ \\ \\ 16 - 4 \sqrt{3} - 4 \sqrt{3} + (\sqrt{3})^2 \\ \\ \\ 16 - 8 \sqrt{3} + (\not \sqrt{3})^\not 2 \\ \\ \\ 16 - 8 \sqrt{3} + 3 \\ \\ \\ => 19 - 8 \sqrt{3}$

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$c) \\ \\(2 + \sqrt{2})^2 * (2- \sqrt{2})^2 \\ \\ \\ (2 + \sqrt{2})*(2 + \sqrt{2}) * (2 -\sqrt{2})*(2 -\sqrt{2}) \\ \\ \\ (6 + 4 \sqrt{2}) * (6 - 4 \sqrt{2} ) \\ \\ \\ 36 - 24 \sqrt{2} - 24\sqrt{2} - 32 \\ \\ \\ 36 - 32 => 4$