Toán Rút gọn biểu thức căn(x-2căn(x-1)) x (căn(x-1)+1) Gấp ạ 26/08/2021 By Daisy Rút gọn biểu thức căn(x-2căn(x-1)) x (căn(x-1)+1) Gấp ạ
$\begin{array}{l}\sqrt{x-2\sqrt{x-1}}.(\sqrt{x-1} +1)\\ =\sqrt{x-1 -2\sqrt{x-1} + 1}.(\sqrt{x-1} +1)\\ =\sqrt{(\sqrt{x-1}-1)^2}.(\sqrt{x-1} +1)\\ =|\sqrt{x-1} -1|.(\sqrt{x-1} +1)\\ =\left[\begin{array}{l}(\sqrt{x-1} -1).(\sqrt{x-1} +1)\,\,\,\,Với \,\,x\geq 2\\-(\sqrt{x-1}-1).(\sqrt{x-1} +1)\,\,\,\,Với\,\,x<2\end{array}\right.\\ =\left[\begin{array}{l}x-2\,\,\,\,Với\,\,x\geq2\\2-x\,\,\,\,Với\,\,x<2\end{array}\right.\end{array}$ Trả lời
Đáp án: $\sqrt{x^{2}-x-2x\sqrt{x-1}+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}$ Giải thích các bước giải: $\sqrt{x-2\sqrt{x-1}}.(\sqrt{x-1}+1)\\=\sqrt{(x-2\sqrt{x-1})(x-1)}+\sqrt{x-2\sqrt{x-1}}\\=\sqrt{x^{2}-x-2x\sqrt{x-1}+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}$ Trả lời
$\begin{array}{l}\sqrt{x-2\sqrt{x-1}}.(\sqrt{x-1} +1)\\ =\sqrt{x-1 -2\sqrt{x-1} + 1}.(\sqrt{x-1} +1)\\ =\sqrt{(\sqrt{x-1}-1)^2}.(\sqrt{x-1} +1)\\ =|\sqrt{x-1} -1|.(\sqrt{x-1} +1)\\ =\left[\begin{array}{l}(\sqrt{x-1} -1).(\sqrt{x-1} +1)\,\,\,\,Với \,\,x\geq 2\\-(\sqrt{x-1}-1).(\sqrt{x-1} +1)\,\,\,\,Với\,\,x<2\end{array}\right.\\ =\left[\begin{array}{l}x-2\,\,\,\,Với\,\,x\geq2\\2-x\,\,\,\,Với\,\,x<2\end{array}\right.\end{array}$
Đáp án: $\sqrt{x^{2}-x-2x\sqrt{x-1}+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}$
Giải thích các bước giải:
$\sqrt{x-2\sqrt{x-1}}.(\sqrt{x-1}+1)\\=\sqrt{(x-2\sqrt{x-1})(x-1)}+\sqrt{x-2\sqrt{x-1}}\\=\sqrt{x^{2}-x-2x\sqrt{x-1}+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}$