Question

Ch.minh 
\(\sqrt{8}\) -\(\dfrac{\sqrt{2}}{\sqrt{2}-1}\) - 2\(\sqrt{\dfrac{1}{2}}\) =2

Answer 1

\(\sqrt{8}-\dfrac{\sqrt{2}}{\sqrt{2}-1}-2\sqrt{\dfrac{1}{2}}\\ =2\sqrt{2}-\dfrac{\sqrt{2}\left(\sqrt{2}+1\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}-\dfrac{2}{\sqrt{2}}\\ =2\sqrt{2}-\dfrac{2+\sqrt{2}}{2-1}-\sqrt{2}\\ =2\sqrt{2}-2-\sqrt{2}-\sqrt{2}\\ =-2\)

Vậy biểu thức bằng -2 nha

Answer 2

Vế trái

\(=\sqrt{2.2^2}-\dfrac{\sqrt{2}\left(\sqrt{2}+1\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}-\dfrac{\left(\sqrt{2}\right)^2}{\sqrt{2}}\)

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

\(=-2\)