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![](https://rs.olm.vn/images/avt/0.png?1311)
\(VT=\frac{\left(5\sqrt{3}+5\sqrt{2}\right).\left(5-2\sqrt{6}\right)}{5\sqrt{3}-5\sqrt{2}}\)
\(=\frac{\left(5\sqrt{3}+5\sqrt{2}\right)^2.\left(5-2\sqrt{6}\right)}{\left(5\sqrt{3}+5\sqrt{2}\right)\left(5\sqrt{3}-5\sqrt{2}\right)}\)\(=\frac{\left(75+50\sqrt{6}+50\right).\left(5-2\sqrt{6}\right)}{75-50}\)
\(=\frac{25\left(5+2\sqrt{6}\right).\left(5-2\sqrt{6}\right)}{25}=5^2-\left(2\sqrt{6}\right)^2\)\(=25-24=1=VP\)
bn chép lại đề nhé
\(=\frac{\left(5\sqrt{3}+5\sqrt{2}\right)\left(5-2\sqrt{6}\right)}{5\sqrt{3}-5\sqrt{2}}\)
\(=\frac{\left(75+50\sqrt{6}+50\right)\left(\sqrt{3}-\sqrt{2}\right)}{75-50}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(VT=\frac{\sqrt{a}\left(\sqrt{a}+\sqrt{b}\right)+b-\sqrt{ab}}{\sqrt{a}+\sqrt{b}}:\left(\frac{a}{\sqrt{b}\left(\sqrt{a}+\sqrt{b}\right)}+\frac{b}{\sqrt{a}\left(\sqrt{b}-\sqrt{a}\right)}-\frac{a+b}{\sqrt{ab}}\right)\)
\(=\frac{a+b}{\sqrt{a}+\sqrt{b}}:\frac{a\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)-b\sqrt{b}\left(\sqrt{a}+\sqrt{b}\right)-\left(a+b\right)\left(a-b\right)}{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}\)
\(=\frac{a+b}{\sqrt{a}+\sqrt{b}}:\frac{a^2-a\sqrt{ab}-b^2-b\sqrt{ab}-a^2+b^2}{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}\)
\(=\frac{a+b}{\sqrt{a}+\sqrt{b}}.\frac{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}{-\left(a+b\right)\sqrt{ab}}=\sqrt{b}-\sqrt{a}=VP\)
Vậy đẳng thức được chứng minh
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\dfrac{\left(5\sqrt{3}+5\sqrt{2}\right)\left(5-2\sqrt{6}\right)}{5\sqrt{3}-5\sqrt{2}}\\ =\dfrac{5\left(\sqrt{3}+\sqrt{2}\right)\left(3-2\sqrt{6}+2\right)}{5\left(\sqrt{3}-\sqrt{2}\right)}\\ =\dfrac{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)^2}{\sqrt{3}-\sqrt{2}}\\ =\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)\\ =3-2\\ =1\)
Vậy \(A=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
a/ \(=\sqrt{\frac{\left(5+\sqrt{21}\right)^2}{\left(5-\sqrt{21}\right)\left(5+\sqrt{21}\right)}}+\sqrt{\frac{\left(5-\sqrt{21}\right)^2}{\left(5-\sqrt{21}\right)\left(5+\sqrt{21}\right)}}\)
\(=\sqrt{\frac{\left(5+\sqrt{21}\right)^2}{4}}+\sqrt{\frac{\left(5-\sqrt{21}\right)^2}{4}}=\frac{5+\sqrt{21}}{2}+\frac{5-\sqrt{21}}{2}\)
\(=\frac{10}{2}=5\)
b/ \(=\left(2-\sqrt{2}\right)\sqrt{2+4\sqrt{3+\sqrt{2}+\sqrt{\left(3-\sqrt{2}\right)^2}}}\)
\(=\left(2-\sqrt{2}\right)\sqrt{2+4\sqrt{3+\sqrt{2}+3-\sqrt{2}}}\)
\(=\left(2-\sqrt{3}\right)\sqrt{2+4\sqrt{6}}\)
Bạn coi lại đề, tới đây ko rút gọn được nữa nên chắc bạn ghi đề nhầm ở chỗ nào đó
c/ \(=\frac{5\left(\sqrt{3}+\sqrt{2}\right)\left(5-\sqrt{24}\right)}{5\left(\sqrt{3}-\sqrt{2}\right)}=\frac{\left(\sqrt{3}+\sqrt{2}\right)^2\left(5-\sqrt{24}\right)}{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}\)
\(=\left(5+2\sqrt{6}\right)\left(5-\sqrt{24}\right)=\left(5+\sqrt{24}\right)\left(5-\sqrt{24}\right)=1\)
d/ Nhân cả tử và mẫu của từng phân số với liên hợp của mẫu, mẫu số sẽ thành 1 hết:
\(=\frac{\sqrt{25}-\sqrt{24}}{\left(\sqrt{25}+\sqrt{24}\right)\left(\sqrt{25}-\sqrt{24}\right)}+\frac{\sqrt{24}-\sqrt{23}}{\left(\sqrt{24}+\sqrt{23}\right)\left(\sqrt{24}-\sqrt{23}\right)}+...+\frac{\sqrt{2}-1}{\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)}\)
\(=\sqrt{25}-\sqrt{24}+\sqrt{24}-\sqrt{23}+...+\sqrt{2}-1\)
\(=\sqrt{25}-1=5-1=4\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{\left(5\sqrt{3}+\sqrt{50}\right)\left(5-2\sqrt{6}\right)}{5\sqrt{3}-5\sqrt{2}}=\frac{\left(5\sqrt{3}+5\sqrt{2}\right)\left(2-2\sqrt{2}.\sqrt{3}+3\right)}{5\left(\sqrt{3}-\sqrt{2}\right)}=\frac{5\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)^2}{5\left(\sqrt{3}-\sqrt{2}\right)}=\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)=\left(\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2=3-2=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\frac{x-1}{2\sqrt{x}}.\frac{\sqrt{x}\left(\sqrt{x}-1\right)^2-\sqrt{x}\left(\sqrt{x}+1\right)^2}{x-1}\)
\(=\frac{\sqrt{x}\left(\sqrt{x}-1-\sqrt{x}-1\right)\left(\sqrt{x}-1+\sqrt{x}+1\right)}{2\sqrt{x}}\)
\(=\frac{-2.2\sqrt{x}}{2}\)
\(=-2\sqrt{x}\)
Thank bạn bài vừa rồi đã k cho mk^^
\(\frac{\left(5\sqrt{3}+\sqrt{50}\right)\left(5-\sqrt{24}\right)}{\sqrt{75}-5\sqrt{2}}\)
\(=\frac{\left(5\sqrt{3}+5\sqrt{2}\right)\left(5-2\sqrt{6}\right)}{5\sqrt{3}-5\sqrt{2}}\)
\(=\frac{5\left(\sqrt{3}+\sqrt{2}\right)\left(3-2.\sqrt{3}.\sqrt{2}+2\right)}{5\left(\sqrt{3}-\sqrt{2}\right)}\)
\(=\frac{5\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)^2}{5\left(\sqrt{3}-\sqrt{2}\right)}\)
\(=\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)=1\)
DÀI QUÁ MK KO GHI ĐƯỢC NÊN VIẾT KQ LUÔN NHA !!!
ĐẲNG THỨC ĐÓ = 1 NHA
Hatsune Miku !