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a) \(\frac{\left(\sqrt{3}-\sqrt{5}\right)^2+4\sqrt{15}}{\sqrt{3}+\sqrt{5}}-\sqrt{5}\)
= \(\frac{3-2\sqrt{15}+5+4\sqrt{15}}{\sqrt{3}+\sqrt{5}}-\sqrt{5}\)
=\(\frac{8+2\sqrt{15}-\sqrt{5}\left(\sqrt{3}+\sqrt{5}\right)}{\sqrt{3}+\sqrt{5}}\)
= \(\frac{8+2\sqrt{15}-\sqrt{15}-\sqrt{25}}{\sqrt{3}+\sqrt{5}}\)
= \(\frac{3+\sqrt{15}}{\sqrt{3}+\sqrt{5}}\)
= \(\frac{\sqrt{3}\left(\sqrt{3}+\sqrt{5}\right)}{\sqrt{3}+\sqrt{5}}\)
= \(\sqrt{3}\)
b) \(\frac{\left(\sqrt{2}+1\right)^2-4\sqrt{2}}{\sqrt{2}-1}.\left(\sqrt{2}+1\right)\)
= \(\frac{2+2\sqrt{2}+1-4\sqrt{2}}{\sqrt{2}-1}.\left(\sqrt{2}+1\right)\)
= \(\frac{\left(\sqrt{2}-1\right)^2.\left(\sqrt{2}+1\right)}{\sqrt{2}-1}\)
= \(\left(\sqrt{2}-1\right).\left(\sqrt{2}+1\right)\)
= 2 - 1
= 1
\(B=\dfrac{21}{2}\left(\sqrt{4+2\sqrt{3}}+\sqrt{6-2\sqrt{5}}\right)^2-3\left(\sqrt{4-2\sqrt{3}}+\sqrt{6+2\sqrt{5}}\right)^2-15\sqrt{15}\)
\(=\dfrac{21}{2}\left(\sqrt{3}+1+\sqrt{5}-1\right)^2-3\left(\sqrt{3}-1+\sqrt{5}+1\right)^2-15\sqrt{15}\)
\(=\dfrac{21}{2}\left(\sqrt{3}+\sqrt{5}\right)^2-3\left(\sqrt{3}+\sqrt{5}\right)^2-15\sqrt{15}\)
\(=\dfrac{15}{2}\left(8+2\sqrt{15}\right)-15\sqrt{15}\)
\(=60+15\sqrt{15}-15\sqrt{15}=60\)
a, = \(\frac{\sqrt{15}}{10}\) + \(\frac{\sqrt{15}}{30}\) - \(\frac{2\sqrt{15}}{15}\)
= \(\sqrt{15}\left(\frac{1}{10}+\frac{1}{30}-\frac{2}{15}\right)\)
= \(\sqrt{15}.0\)
= 0
b, = \(\left(\frac{\sqrt{5}+\sqrt{3}}{5-3}+\frac{\sqrt{5}-\sqrt{3}}{5-3}\right).\sqrt{5}\)
= \(\frac{\sqrt{5}+\sqrt{3}+\sqrt{5}-\sqrt{3}}{2}.\sqrt{5}\)
= \(\frac{2\sqrt{5}}{2}.\sqrt{5}\)
= \(\sqrt{5}.\sqrt{5}\)
= 5
c, = \(\frac{5\sqrt{3}}{\sqrt{15}}+\frac{3\sqrt{5}}{\sqrt{15}}\)
= \(\sqrt{5}+\sqrt{3}\)
d, Mình sửa lại đề bài cho bạn : \(\left(2+\sqrt{5}\right)^2-\left(2-\sqrt{5}\right)^2\)
= \(\left(2+\sqrt{5}-2+\sqrt{5}\right)\left(2+\sqrt{5}+2-\sqrt{5}\right)\)
= \(2\sqrt{5}.4\)
= \(8\sqrt{5}\)
e, = \(\frac{4\sqrt{3}}{3}+15\sqrt{3}-3\sqrt{3}-\frac{20\sqrt{3}}{3}\)
= \(\sqrt{3}.\left(\frac{4}{3}+15-3-\frac{20}{3}\right)\)
= \(\sqrt{3}.\frac{20}{3}\)
= \(\frac{20\sqrt{3}}{3}\)
a, 320+160−2115
b, (15−3+15+3).5
c, (53+35):15
d, (2+5)2−(2+5)2
e, 1348+375−27−10113
