Question

1. Tìm giá trị nhỏ nhất của M:

M = \(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+15+8\sqrt{x-1}}\)

2. Rút gọn:

A= \(\sqrt{\sqrt{28-16\sqrt{3}}}-\sqrt{\sqrt{28+16\sqrt{3}}}\)

B= \(\sqrt{5-2\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)

Answer 1

2.

A=\(\sqrt{\sqrt{\left(\sqrt{16}-\sqrt{12}\right)^2}}-\sqrt{\sqrt{\left(\sqrt{16}+\sqrt{12}\right)^2}}\)

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

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

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

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

\(=-2\)

B= \(\sqrt{5-2\sqrt{2+\sqrt{\left(\sqrt{8}+\sqrt{1}\right)^2}}}\)

\(=\sqrt{5-2\sqrt{2+\sqrt{8}+1}}\)

\(=\sqrt{5-2\sqrt{3+2\sqrt{2}}}\)

\(=\sqrt{5-2\sqrt{\left(\sqrt{2}+\sqrt{1}\right)^2}}\)

\(=\sqrt{5-2\sqrt{2}-2}\)

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

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

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