Question

a) x- 2y- \(\sqrt{x^2-4xy+4y^2}\) với x = \(\sqrt{5}-1\);y = \(\sqrt{2}-1\)

b) \(\sqrt{x^2-8x+16}\) - \(\sqrt{x^2-4x+4}\) với x = 3\(\sqrt{2}\) -1

c) \(\sqrt{x+2\sqrt{x}+1}\) +\(\sqrt{x-2\sqrt{x}-1}\) với x = \(2\sqrt{7}+9\)

Answer 1

a: \(=\sqrt{5}-1-2\left(\sqrt{2}-1\right)-\left|\sqrt{5}-1-2\left(\sqrt{2}-1\right)\right|\)

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

\(=-2\sqrt{2}+\sqrt{5}+1-\left(-2\sqrt{2}+\sqrt{5}+1\right)=0\)

b: \(=\left|x-4\right|-\left|x-2\right|\)

\(=\left|3\sqrt{2}-1-4\right|-\left|3\sqrt{2}-1-2\right|\)

\(=\left|3\sqrt{2}-5\right|-\left|3\sqrt{2}-3\right|\)

\(=5-3\sqrt{2}-3\sqrt{2}+3=8-6\sqrt{2}\)