\(12\sqrt{\dfrac{1}{2}}+\dfrac{\sqrt{2}}{\sqrt{2}-1}-7\sqrt{\left(1-\sqrt{2}\right)^2}\)
\(=\sqrt{12^2.\dfrac{1}{2}}+\dfrac{\sqrt{2}\left(\sqrt{2}+1\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}-7\left|\sqrt{2}-1\right|\) (Vì 1< \(\sqrt{2}\))
\(=\sqrt{6^2.2^2.\dfrac{1}{2}}+\dfrac{2+\sqrt{2}}{\left(\sqrt{2}\right)^2-1^2}-7\left(\sqrt{2}-1\right)\)
\(=6\sqrt{2}+2+\sqrt{2}-7\sqrt{2}+7\)
\(=\left(6\sqrt{2}+\sqrt{2}-7\sqrt{2}\right)+\left(2+7\right)\)
\(=9\)
= \(6\sqrt{2}+2+\sqrt{2}-7\left|1-\sqrt{2}\right|\)
= \(6\sqrt{2}+2+\sqrt{2}-7.\sqrt{2}-1\)
= 1
`12 sqrt{1/2}+sqrt2/(sqrt2-1)-7sqrt{(1-sqrt2)^2}`
`= 12/sqrt2+sqrt2(sqrt2+1)-7|1-sqrt2|`
`= 6sqrt2+2+sqrt2-7(sqrt2-1)` (`1-sqrt2<0`)
`= 6sqrt2+2+sqrt2-7sqrt2+7`
`= 9`
