\(\sqrt{12}-6\sqrt{\dfrac{1}{3}}-\dfrac{4}{2-\sqrt{3}}\)
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19 tháng 10 2023

\(A=3\sqrt{12}-6\sqrt{\dfrac{1}{3}}-\dfrac{4}{2-\sqrt{3}}\\ A=6\sqrt{3}-\dfrac{6}{\sqrt{3}}-\dfrac{4\left(2+\sqrt{3}\right)}{4-3}\\ =6\sqrt{3}-2\sqrt{3}-8-4\sqrt{3}\\ -8\)

a: \(=\dfrac{2\sqrt{7}-10-6+2\sqrt{7}}{4}+4+2\sqrt{7}-\dfrac{20}{9}+\dfrac{5}{9}\sqrt{7}\)

\(=\sqrt{7}-4+4+2\sqrt{7}-\dfrac{20}{9}+\dfrac{5}{9}\sqrt{7}\)

\(=\dfrac{32}{9}\sqrt{7}-\dfrac{20}{9}\)

b: \(=\dfrac{2\sqrt{6}+4+2\sqrt{6}-4}{2}+\dfrac{5\sqrt{6}}{6}\)

\(=2\sqrt{6}+\dfrac{5}{6}\sqrt{6}=\dfrac{17}{6}\sqrt{6}\)

a: \(=2\cdot\dfrac{4}{3}\sqrt{3}-3\cdot\dfrac{1}{9}\sqrt{3}-6\cdot\dfrac{2}{15}\sqrt{3}\)

\(=\dfrac{8}{3}\sqrt{3}-\dfrac{1}{3}\sqrt{3}-\dfrac{4}{5}\sqrt{3}=\dfrac{23}{15}\sqrt{3}\)

b: \(=\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(2+\sqrt{3}\right)^2}\)

\(=2-\sqrt{3}+2+\sqrt{3}=4\)

c: \(=6\sqrt{3}-4\sqrt{3}+\dfrac{3}{5}\cdot5\sqrt{3}=2\sqrt{3}+3\sqrt{3}=5\sqrt{3}\)

1: \(=\sqrt{5}-\dfrac{\sqrt{5}}{2}=\dfrac{\sqrt{5}}{2}\)

2: \(=\dfrac{4+2\sqrt{3}+4-2\sqrt{3}}{2}=\dfrac{8}{2}=4\)

4: \(=\dfrac{-3+5\sqrt{3}}{11}+\dfrac{3+5\sqrt{3}}{11}=\dfrac{10\sqrt{3}}{11}\)

a: \(=\left(5+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)^2\cdot\left(\sqrt{3}-\sqrt{2}\right)\)

\(=\left(5-2\sqrt{6}\right)\left(\sqrt{3}-\sqrt{2}\right)\)

\(=5\sqrt{3}-5\sqrt{2}-6\sqrt{2}+4\sqrt{3}=9\sqrt{3}-11\sqrt{2}\)

b: \(=\dfrac{\sqrt{2}}{2+\sqrt{3}+1}+\dfrac{\sqrt{2}}{2-\sqrt{3}+1}\)

\(=\dfrac{\sqrt{2}}{3+\sqrt{3}}+\dfrac{\sqrt{2}}{3-\sqrt{3}}\)

\(=\dfrac{3\sqrt{2}-\sqrt{6}+3\sqrt{2}+\sqrt{6}}{9-3}=\dfrac{6\sqrt{2}}{6}=\sqrt{2}\)

d: \(=2\sqrt{2}-\sqrt{6}-3\sqrt{2}+\sqrt{6}=-\sqrt{2}\)

25 tháng 12 2017

Rút gọn biểu thức chứa căn bậc hai

6 tháng 9 2018

\(a.\left(\dfrac{\sqrt{6}-\sqrt{3}}{5\sqrt{2}-5}+\dfrac{\sqrt{5}}{5}\right):\dfrac{2}{\sqrt{5}-\sqrt{3}}=\left[\dfrac{\sqrt{3}\left(\sqrt{2}-1\right)}{5\left(\sqrt{2}-1\right)}+\dfrac{\sqrt{5}}{5}\right]:\dfrac{2\left(\sqrt{5}+\sqrt{3}\right)}{2}=\dfrac{\sqrt{3}+\sqrt{5}}{5}.\dfrac{1}{\sqrt{5}+\sqrt{3}}=\dfrac{1}{5}\)

\(b.\dfrac{\sqrt{6}-3}{\sqrt{3}-\sqrt{2}}-\dfrac{4}{\sqrt{3}+1}+3\sqrt{3}=\dfrac{-\sqrt{3}\left(\sqrt{3}-\sqrt{2}\right)}{\sqrt{3}-\sqrt{2}}-\dfrac{4}{\sqrt{3}+1}+3\sqrt{3}=2\sqrt{3}-\dfrac{4}{\sqrt{3}+1}=\dfrac{2\sqrt{3}\left(\sqrt{3}+1\right)-4}{\sqrt{3}+1}=\dfrac{2+2\sqrt{3}}{\sqrt{3}+1}=\dfrac{2\left(1+\sqrt{3}\right)}{1+\sqrt{3}}=2\)

6 tháng 9 2018

a. \(2\sqrt{16}+\sqrt{2}.\sqrt{0,02}-\dfrac{\sqrt{12,1}}{\sqrt{0,1}}=2.4+\sqrt{0,04}-\sqrt{\dfrac{12,1}{0,1}}=8+0,2-11=-2,8\)b. \(5\sqrt{20}-4\sqrt{45}+\dfrac{15}{\sqrt{5}}=10\sqrt{5}-12\sqrt{5}+3\sqrt{5}=\sqrt{5}\)

c. \(\left(\dfrac{\sqrt{6}-\sqrt{3}}{5\sqrt{2}-5}+\dfrac{\sqrt{5}}{5}\right):\dfrac{2}{\sqrt{5}-\sqrt{3}}=\left(\dfrac{\sqrt{3}\left(\sqrt{2}-1\right)}{5\left(\sqrt{2}-1\right)}+\dfrac{\sqrt{5}}{5}\right).\dfrac{\sqrt{5}-\sqrt{3}}{2}=\dfrac{\sqrt{3}+\sqrt{5}}{5}.\dfrac{\sqrt{5}-\sqrt{3}}{2}=\dfrac{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}{5.2}=\dfrac{5-3}{10}=\dfrac{2}{10}=\dfrac{1}{5}\)d. \(\dfrac{\sqrt{6}-3}{\sqrt{3}-\sqrt{2}}-\dfrac{4}{\sqrt{3}+1}+3\sqrt{3}=\dfrac{-\sqrt{3}\left(\sqrt{3}-\sqrt{2}\right)}{\sqrt{3}-\sqrt{2}}-\dfrac{4}{\sqrt{3}+1}+3\sqrt{3}=3\sqrt{3}-\sqrt{3}-\dfrac{4}{\sqrt{3}+1}=\dfrac{\left(\sqrt{3}+1\right).2\sqrt{3}-4}{\sqrt{3}+1}=\dfrac{6+2\sqrt{3}-4}{\sqrt{3}+1}=\dfrac{2+2\sqrt{3}}{\sqrt{3}+1}=\dfrac{ 2\left(\sqrt{3}+1\right)}{\sqrt{3}+1}=2\)

a: \(=4\sqrt{5}-\left|2-\sqrt{5}\right|+\sqrt{\dfrac{16}{5}}\)

\(=4\sqrt{5}-\sqrt{5}+2+\dfrac{4}{5}\sqrt{5}\)

\(=\dfrac{19}{5}\sqrt{5}+2\)

b: \(=\dfrac{-\sqrt{3}\left(1-\sqrt{2}\right)}{1-\sqrt{2}}+\dfrac{\sqrt{3}\left(6+\sqrt{3}\right)}{\sqrt{3}}-\dfrac{13\left(4-\sqrt{3}\right)}{\left(4-\sqrt{3}\right)\left(4+\sqrt{3}\right)}\)

\(=-\sqrt{3}+6+\sqrt{3}-4+\sqrt{3}=2+\sqrt{3}\)

1: \(=\left(\dfrac{4}{3}\sqrt{3}+\sqrt{2}+\sqrt{\dfrac{10}{3}}\right)\cdot\left(\sqrt{\dfrac{6}{5}}+\sqrt{2}-\dfrac{4}{\sqrt{5}}\right)\)

\(=\left(\dfrac{4\sqrt{3}}{3}+\dfrac{3\sqrt{2}}{3}+\dfrac{\sqrt{30}}{3}\right)\cdot\left(\dfrac{\sqrt{30}}{5}+\dfrac{5\sqrt{2}}{5}-\dfrac{4\sqrt{5}}{5}\right)\)

\(=\dfrac{\left(4\sqrt{3}+3\sqrt{2}+\sqrt{30}\right)\left(\sqrt{30}+5\sqrt{2}-4\sqrt{5}\right)}{15}\)

2: \(=\left(2\sqrt{3}+6\sqrt{3}\right)\cdot\dfrac{\sqrt{3}}{2}-5\sqrt{6}\)

\(=\dfrac{8\sqrt{9}}{2}-5\sqrt{6}=4\sqrt{9}-5\sqrt{6}=12-5\sqrt{6}\)

12 tháng 10 2018

Giải phương trình

<=> |2x - 1| - 2 = x <=> |2x - 1| = x + 2

TH1: 2x - 1 = x + 2

Tự giải: x = 3

TH2: 1 - 2x = x + 2

Tự giải: x = -1/3

(Nhớ thêm điều kiện nhá)

12 tháng 10 2018

À nhầm, không cần điều kiện nha