Question

B1:Thực hiện phép tính
a, A= \(\sqrt{(1-\sqrt{2)}^2}-\sqrt{18}\)
b, B=\(\frac{\sqrt{2}-2}{1-\sqrt{2}}+\sqrt{50}\)
c, C=\(\frac{3}{\sqrt{2}-1}-\frac{3}{\sqrt{2}+1}\)

Answer 1

\(A=\sqrt{\left(1-\sqrt{2}\right)^2}-\sqrt{18}=\left|1-\sqrt{2}\right|-\sqrt{18}\)

\(=\sqrt{2}-1-\sqrt{2\cdot9}=\sqrt{2}-3\sqrt{2}-1=-2\sqrt{2}-1=-\left(1+\sqrt{2}\right)\)

\(B=\frac{\sqrt{2}-2}{1-\sqrt{2}}+\sqrt{50}=\frac{\sqrt{2}\left(1-\sqrt{2}\right)}{1-\sqrt{2}}+\sqrt{50}=\sqrt{2}+\sqrt{2\cdot25}=6\sqrt{2}\)

\(C=\frac{3}{\sqrt{2}-1}-\frac{3}{\sqrt{2}+1}=3\cdot\frac{\sqrt{2}+1-\left(\sqrt{2}-1\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}=3\cdot2=6\)