Question

1)Rút gọn:

P=\(\dfrac{2-\sqrt{6}}{3-\sqrt{6}}\)

2)Tính M= \(\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\)

Answer 1

Câu 2:

\(M=\dfrac{\sqrt{4-2\sqrt{3}}-\sqrt{4+2\sqrt{3}}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{3}-1-\sqrt{3}-1}{\sqrt{2}}=-\dfrac{2}{\sqrt{2}}=-\sqrt{2}\)

Answer 2

\(P=\dfrac{\left(2-\sqrt{6}\right)\left(3+\sqrt{6}\right)}{\left(3-\sqrt{6}\right)\left(3+\sqrt{6}\right)}=\dfrac{6+2\sqrt{6}-3\sqrt{6}-6}{3^2-6}=\dfrac{-\sqrt{6}}{3}\)

\(M=\dfrac{\sqrt{3-2\sqrt{3}+1}-\sqrt{3+2\sqrt[]{3}+1}}{\sqrt{2}}=\dfrac{\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{\left(\sqrt{3}+1\right)^2}}{\sqrt{2}}=\dfrac{\sqrt{3}-1-\sqrt{3}-1}{\sqrt{2}}=\dfrac{-2}{\sqrt{2}}=-\sqrt{2}\)\(\sqrt{ }\)