Question

Usando a multiplicação, calcule: 
a) (1+√5)²       b) (2-√3)²

Answer 1

Temos que:

$(a+b)^2=a^2+2ab+b^2$ e 

$(a-b)^2=a^2-2ab+b^2$

Assim:

a) $(1+\sqrt{5})^2=1^2+2\cdot1\cdot\sqrt{5}+(\sqrt{5})^2=1+2\sqrt{5}+5=6+2\sqrt{5}$ e 

b) $(2-\sqrt{3})^2=2^2-2\cdot2\cdot\sqrt{3}+(\sqrt{3})^2=4-4\sqrt{3}+3=7-4\sqrt{3}$.

Answer 2

$a) \\ (1 + \sqrt{5})^2 \\ \\ (1 + \sqrt{5}) * (1 + \sqrt{5}) \\ \\ 1 + 1* \sqrt{5} + 1* \sqrt{5} + 5 \\ \\ 6 + 2 \sqrt{5}$

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$b) \\ (2 - \sqrt{3})^2 \\ \\ (2 - \sqrt{3}) * (2 - \sqrt{3}) \\ \\ 4 - 2 \sqrt{3} - 2 \sqrt{3} + 3 \\ \\ 7 -4 \sqrt{3}$