Question

por favor não excluem a pergunta,responda ela ❤
qual é o valor dá expressão
√3+1/√3-1 + √3-1/√3+1
a)√3
b)4
c)3
d)2
e)√2

Answer 1

$(\sqrt{3}+1)\cdot(\sqrt{3}+1)= \sqrt{9} + \sqrt{3} + \sqrt{3} +1=3+2 \sqrt{3}+1=4+2 \sqrt{3} \\ \\(\sqrt{3}-1)\cdot(\sqrt{3}-1)= \sqrt{9} - \sqrt{3} - \sqrt{3} +1=3-2 \sqrt{3}+1=4-2 \sqrt{3} \\ \\(\sqrt{3}+1)\cdot(\sqrt{3}-1)= \sqrt{9} - \sqrt{3} + \sqrt{3} -1=3-1=2$

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$\\\frac{\sqrt{3}+1}{\sqrt{3}-1}=\frac{\sqrt{3}+1}{\sqrt{3}-1} \cdot\frac{\sqrt{3}+1}{\sqrt{3}+1} =\frac{(\sqrt{3}+1)\cdot(\sqrt{3}+1)}{(\sqrt{3}-1)\cdot(\sqrt{3}+1)} = \frac{4+2 \sqrt{3}}{2} \\ \\ \\ \\\frac{\sqrt{3}-1}{\sqrt{3}+1}=\frac{\sqrt{3}-1}{\sqrt{3}+1} \cdot\frac{\sqrt{3}-1}{\sqrt{3}-1} =\frac{(\sqrt{3}-1)\cdot(\sqrt{3}-1)}{(\sqrt{3}+1)\cdot(\sqrt{3}-1)} = \frac{4-2 \sqrt{3}}{2}$

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$\\\frac{\sqrt{3}+1}{\sqrt{3}-1} + \frac{\sqrt{3}-1}{\sqrt{3}+1} = \frac{4+2 \sqrt{3}}{2} + \frac{4-2 \sqrt{3}}{2} = \frac{4+2 \sqrt{3}+4-2 \sqrt{3}}{2} = \frac{8}{2} = 4$