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24 tháng 8 2023
a: \(P=\dfrac{\sqrt{3}\left(2+\sqrt{3}\right)}{\sqrt{3}}+\dfrac{\sqrt{2}\left(\sqrt{2}-1\right)}{1}-\sqrt{3}-\sqrt{2}\)
\(=2+\sqrt{3}+2-\sqrt{2}-\sqrt{3}-\sqrt{2}\)
\(=4-2\sqrt{2}\)
b: \(N=\left(1-\dfrac{\sqrt{5}\left(\sqrt{5}+1\right)}{\sqrt{5}+1}\right)\left(\dfrac{-\sqrt{5}\left(1-\sqrt{5}\right)}{1-\sqrt{5}}-1\right)\)
\(=\left(1-\sqrt{5}\right)\left(-\sqrt{5}-1\right)\)
\(=\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)=5-1=4\)
21 tháng 7 2021
bạn viết rõ đề ra nhé
a, \(\left|3x+1\right|-x-5=0\Leftrightarrow\left|3x+1\right|=x+5\)ĐK : \(x\ge-5\)
TH1 : \(3x+1=x+5\Leftrightarrow x=2\)( tm )
TH2 : \(3x+1=-x-5\Leftrightarrow x=-\dfrac{3}{2}\)( tm )
9 tháng 10 2021
4: Ta có: \(\dfrac{1}{3+\sqrt{5}}-\dfrac{1}{3-\sqrt{5}}\)
\(=\dfrac{3-\sqrt{5}-3-\sqrt{5}}{4}\)
\(=\dfrac{-\sqrt{5}}{2}\)
IK
1
30 tháng 6 2023
a: \(=\left(1+\dfrac{\sqrt{5}\left(\sqrt{5}-1\right)}{-\left(\sqrt{5}-1\right)}\right)\left(\sqrt{5}+1\right)\)
=(1-căn 5)(1+căn 5)
=1-5=-4
b: \(=\sqrt{3}+\sqrt{2}+\sqrt{3}-\sqrt{2}=2\sqrt{3}\)
HP
29 tháng 8 2021
11.
\(\dfrac{5+\sqrt{5}}{5-\sqrt{5}}+\dfrac{5-\sqrt{5}}{5+\sqrt{5}}\)
\(=\dfrac{\left(5+\sqrt{5}\right)^2}{\left(5-\sqrt{5}\right)\left(5+\sqrt{5}\right)}+\dfrac{\left(5-\sqrt{5}\right)^2}{\left(5-\sqrt{5}\right)\left(5+\sqrt{5}\right)}\)
\(=\dfrac{25+5+10\sqrt{5}}{20}+\dfrac{25+5-10\sqrt{5}}{20}\)
\(=3\)
HP
29 tháng 8 2021
12.
\(\dfrac{3+2\sqrt{3}}{\sqrt{3}}+\dfrac{2+\sqrt{2}}{\sqrt{2}+1}-\dfrac{1}{2-\sqrt{3}}\)
\(=\dfrac{\sqrt{3}\left(\sqrt{3}+2\right)}{\sqrt{3}}+\dfrac{\sqrt{2}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}-\dfrac{2+\sqrt{3}}{4-3}\)
\(=\sqrt{3}+2+\sqrt{2}-2-\sqrt{3}\)
\(=\sqrt{2}\)
9 tháng 10 2021
1: ta có: \(\dfrac{1}{3-2\sqrt{2}}+\dfrac{1}{\sqrt{5}+2}\)
\(=3+2\sqrt{2}+\sqrt{5}-2\)
\(=2\sqrt{2}+\sqrt{5}+1\)
2: Ta có: \(\dfrac{1}{3-2\sqrt{2}}-\dfrac{1}{3+2\sqrt{2}}\)
\(=3+2\sqrt{2}-3+2\sqrt{2}\)
\(=4\sqrt{2}\)
H
2
29 tháng 8 2023
2: \(\dfrac{\sqrt{12}-\sqrt{5}}{\sqrt{2}-1}-\dfrac{1}{\sqrt{5}-2}\)
\(=\left(2\sqrt{3}-\sqrt{5}\right)\left(\sqrt{2}+1\right)-\sqrt{5}-2\)
\(=2\sqrt{6}+2\sqrt{3}-\sqrt{10}-\sqrt{5}-\sqrt{5}-2\)
\(=2\sqrt{6}+2\sqrt{3}-\sqrt{10}-2\sqrt{5}-2\)
3: \(=2\cdot3\sqrt{3}-6\cdot\dfrac{1}{\sqrt{3}}+2-\sqrt{3}-3\sqrt{3}\)
\(=6\sqrt{3}-2\sqrt{3}+2-4\sqrt{3}=2\)
H9
HT.Phong (9A5)
CTVHS
30 tháng 8 2023
1) \(\dfrac{3+\sqrt{3}}{\sqrt{5}}-\dfrac{2}{\sqrt{3}-1}\)
\(=\dfrac{\sqrt{5}\cdot\left(3+\sqrt{3}\right)}{\sqrt{5}\cdot\sqrt{5}}-\dfrac{2\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}\)
\(=\dfrac{3\sqrt{5}+\sqrt{15}}{5}-\dfrac{2\left(\sqrt{3}-1\right)}{3-1}\)
\(=\dfrac{3\sqrt{5}+\sqrt{15}}{5}-\left(\sqrt{3}-1\right)\)
\(=\dfrac{3\sqrt{5}+\sqrt{15}-5\sqrt{3}+5}{5}\)
2) \(\dfrac{\sqrt{12}-\sqrt{5}}{\sqrt{2}-1}-\dfrac{1}{\sqrt{5}-2}\)
\(=\dfrac{\left(2\sqrt{3}-\sqrt{5}\right)\left(\sqrt{2}+1\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}-\dfrac{\sqrt{5}+2}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}\)
\(=\dfrac{2\sqrt{6}+2\sqrt{3}-\sqrt{10}-\sqrt{5}}{2-1}-\dfrac{\sqrt{5}+2}{5-4}\)
\(=2\sqrt{6}+2\sqrt{3}-\sqrt{10}-\sqrt{5}-\left(\sqrt{5}+2\right)\)
\(=2\sqrt{6}+2\sqrt{3}-\sqrt{10}-2\sqrt{5}-2\)
3) \(2\sqrt{27}-6\sqrt{\dfrac{1}{3}}+\dfrac{1}{2}+\dfrac{\sqrt{3}-9}{\sqrt{3}}\)
\(=2\cdot3\sqrt{3}-\dfrac{6}{\sqrt{3}}+\dfrac{1}{2}+\dfrac{\sqrt{3}\left(1-3\sqrt{3}\right)}{\sqrt{3}}\)
\(=6\sqrt{3}-\dfrac{\sqrt{3}\cdot2\sqrt{3}}{\sqrt{3}}+\dfrac{1}{2}+1-3\sqrt{3}\)
\(=6\sqrt{3}-2\sqrt{3}+\dfrac{1}{2}+1-3\sqrt{3}\)
\(=\dfrac{1}{2}+1+\sqrt{3}\)
\(=\dfrac{3}{2}+\sqrt{3}\)
T
28 tháng 8 2023
\(\dfrac{\sqrt{6}-\sqrt{3}}{\sqrt{2}-1}+\dfrac{3+\sqrt{3}}{\sqrt{3}+1}+\dfrac{2}{\sqrt{2}+1}-\dfrac{4}{\sqrt{2}}\)
\(=\dfrac{\sqrt{3}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}+\dfrac{\sqrt{3}\left(\sqrt{3}+1\right)}{\sqrt{3}+1}+\dfrac{2\sqrt{2}}{2+\sqrt{2}}-\dfrac{4\sqrt{2}+4}{2+\sqrt{2}}\)
\(=\sqrt{3}+\sqrt{3}+\dfrac{-2\sqrt{2}-4}{2+\sqrt{2}}\)
\(=2\sqrt{3}+\dfrac{-2\left(2+\sqrt{2}\right)}{2+\sqrt{2}}\)
\(=2\sqrt{3}-2\)
\(------\)
\(\dfrac{4}{\sqrt{5}+1}+\dfrac{5}{\sqrt{5}+2}+\dfrac{5}{\sqrt{5}+3}\)
\(=\dfrac{4\left(\sqrt{5}-1\right)}{\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)}+\dfrac{5\left(\sqrt{5}-2\right)}{\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)}+\dfrac{5\left(\sqrt{5}-3\right)}{\left(\sqrt{5}+3\right)\left(\sqrt{5}-3\right)}\)
\(=\dfrac{4\sqrt{5}-4}{5-1}+\dfrac{5\sqrt{5}-10}{5-4}+\dfrac{5\sqrt{5}-15}{5-9}\)
\(=5\sqrt{5}-10+\left(\dfrac{4\sqrt{5}-4}{4}+\dfrac{5\sqrt{5}-15}{-4}\right)\)
\(=\dfrac{4\cdot\left(5\sqrt{5}-10\right)}{4}+\left(\dfrac{4\sqrt{5}-4}{4}-\dfrac{5\sqrt{5}-15}{4}\right)\)
\(=\dfrac{20\sqrt{5}-40}{4}+\dfrac{-\sqrt{5}+11}{4}\)
\(=\dfrac{19\sqrt{5}-29}{4}\)
#Ayumu
\(\sqrt{\left(\sqrt{5}-3\right)^2}-\sqrt{\frac{1}{5}}\)
\(\Leftrightarrow|\sqrt{5}-3|-\sqrt{\frac{1}{5}}\)
\(\Leftrightarrow3-\sqrt{5}-\sqrt{\frac{1}{5}}\)
\(\Leftrightarrow\frac{15}{5}-\frac{5\sqrt{5}}{5}-\frac{\sqrt{5}}{5}\)
\(\Leftrightarrow\frac{15-5\sqrt{5}-\sqrt{5}}{5}\)
\(\Leftrightarrow\frac{15-6\sqrt{5}}{5}.\)