q, \(Q=\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\)
\(=>Q\sqrt{2}=\sqrt{4-2\sqrt{3}}-\sqrt{4+2\sqrt{3}}\)
\(Q\sqrt{2}=\sqrt{\left(\sqrt{3}\right)^2-2\sqrt{3}+1}-\sqrt{\left(\sqrt{3}\right)^2+2\sqrt{3}+1}\)
\(Q\sqrt{2}=\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{\left(\sqrt{3}+1\right)^2}=\sqrt{3}-1-\sqrt[]{3}-1=-2\)
\(=>Q=\dfrac{-2}{\sqrt{2}}=-\sqrt{2}\)
b, đặt \(A=\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
\(=>A^2=12-3\sqrt{7}+12+3\sqrt{7}-2\sqrt{\left(12-3\sqrt{7}\right)\left(12+3\sqrt{7}\right)}\)
\(A^2=24-2\sqrt{12^2-\left(3\sqrt{7}\right)^2}=24-2\sqrt{81}=24-2.9=6\)
\(=>A=\sqrt{6}\)
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