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Câu 1,2,3 Ez quá rồi :3
Câu 4:
Tổng quát:
\(\frac{1}{\sqrt{a}+\sqrt{a+1}}=\frac{\sqrt{a}-\sqrt{a+1}}{a-a-1}=\sqrt{a+1}-\sqrt{a}.\) Game là dễ :v
Câu 5 ko khác câu 4 lắm :v
Câu 5:
Tổng quát:
\(\frac{1}{\sqrt{a}-\sqrt{a+1}}=\frac{\sqrt{a}+\sqrt{a+1}}{a-a-1}=-\sqrt{a}-\sqrt{a+1}.\) Game là dễ :v
b) \(B=\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+2+2}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{4}+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)+\left(\sqrt{4}+\sqrt{6}+\sqrt{8}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)+\sqrt{2}.\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)\left(\sqrt{2}+1\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\sqrt{2}+1\)
c) \(C=\sqrt{3+2\sqrt{2}}+\sqrt{6-4\sqrt{2}}\)
\(=\sqrt{2+2\sqrt{2}+1}+\sqrt{4-4\sqrt{2}+2}\)
\(=\sqrt{\left(\sqrt{2}+1\right)^2}+\sqrt{\left(2-\sqrt{2}\right)^2}\)
\(=\left|\sqrt{2}+1\right|+\left|2-\sqrt{2}\right|\)
\(=\sqrt{2}+1+2-\sqrt{2}=3\)
1, \(=\frac{4\sqrt{2}\left(2-\sqrt{2}\right)}{2^2-\sqrt{2}^2}-\frac{4\sqrt{2}\left(2+\sqrt{2}\right)}{2^2-\sqrt{2}^2}\)
=\(\frac{4\sqrt{2}\left(2-\sqrt{2}\right)}{2}-\frac{4\sqrt{2}\left(2+\sqrt{2}\right)}{2}\)
=\(2\sqrt{2}\left(2-\sqrt{2}\right)-2\sqrt{2}\left(2+\sqrt{2}\right)\)
=\(4\sqrt{2}-4-4\sqrt{2}-4\)
=-8
2, =\(\sqrt{2}+\sqrt{2}-2.3\sqrt{2}+\left|1-\sqrt{2}\right|\)
= \(-4\sqrt{2}+1-\sqrt{2}\) = \(1-5\sqrt{2}\)
3, =\(9\sqrt{\frac{2.2}{3.2}}+5\sqrt{9.6}-\sqrt{\frac{1}{6}}\)
=\(3\sqrt{6}+15\sqrt{6}-\frac{1}{6}\sqrt{6}\)
=\(\frac{107}{6}\sqrt{6}\)
4, =\(\sqrt{\left(4+2\sqrt{2}\right)\left(4-2\sqrt{2}\right)}.\left(2\sqrt{2}-\sqrt{2}\right)\)
= \(\sqrt{4^2-\left(2\sqrt{2}\right)^2}.\sqrt{2}\)
= \(\sqrt{16-8}.\sqrt{2}\)
= \(\sqrt{8}.\sqrt{2}=\sqrt{16}=4\)
5, = \(\sqrt{9-2.3.\sqrt{5}+5}+\sqrt{1-2.1.\sqrt{2}+2}+\sqrt{5-2.\sqrt{2}.\sqrt{5}+2}\)
\(=\sqrt{\left(3-\sqrt{5}\right)^2}+\sqrt{(1-\sqrt{2})^2}+\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}\)\(=\left|3-\sqrt{5}\right|+\left|1-\sqrt{2}\right|+\left|\sqrt{5}-\sqrt{2}\right|\)
\(=3-\sqrt{5}+1-\sqrt{2}+\sqrt{5}-\sqrt{2}\)
\(=4-2\sqrt{2}\)
Thêm câu này hộ tớ nx nhé !
e) \(\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right).\left(\sqrt{2}-3\sqrt{0.4}\right)\)
\(a,\left(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3}\right)\cdot\frac{1}{\sqrt{6}}\)
\(=\left(\frac{\sqrt{12}-\sqrt{6}}{2\left(\sqrt{2}-1\right)}-\frac{6\sqrt{6}}{3}\right)\cdot\frac{1}{\sqrt{6}}\)
\(=\left(\frac{\sqrt{6}\left(\sqrt{2}-1\right)}{2\left(\sqrt{2}-1\right)}-2\sqrt{6}\right)\cdot\frac{1}{\sqrt{6}}\)
\(=\left(\frac{\sqrt{6}}{2}-\frac{4\sqrt{6}}{2}\right)\cdot\frac{1}{\sqrt{6}}\)
\(=\frac{\sqrt{6}-4\sqrt{6}}{2}\cdot\frac{1}{\sqrt{6}}\)
\(=\frac{-3\sqrt{6}}{2}\cdot\frac{1}{\sqrt{6}}\)
\(=-\frac{3}{2}\)
Ai lam ho voi minh dang can lam
ai làm hộ với mình đang cần gấp