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29 tháng 10 2021

\(=2\sqrt{3a}-5\sqrt{3a}+\dfrac{3}{2}\sqrt{3a}-10\sqrt{3a}\)

\(=-\dfrac{23}{2}\sqrt{3a}\)

15 tháng 12 2019

\(2\sqrt{3a}-\sqrt{75a}+a\sqrt{\frac{6}{5}.\frac{5}{2a}}-\frac{2}{5}\sqrt{300a^3}\)

\(=2\sqrt{3a}-5\sqrt{3a}+a\sqrt{\frac{3}{2}}-\frac{2}{5}.10.a\sqrt{3a}\)

\(=-3\sqrt{3a}+\sqrt{\frac{3}{a}.a^2-4\sqrt{3a}}\)

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

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

\(=-2\sqrt{3a}\left(1+2a\right)\)

15 tháng 7 2017

a) \(\left(2-\sqrt{2}\right)\left(-5\sqrt{2}\right)-\left(3\sqrt{2}-5\right)^2\)

\(=-10\sqrt{2}+5.2-\left(18-30\sqrt{2}+25\right)\)

\(=-10\sqrt{2}+10-18+30\sqrt{2}-25\)

\(=20\sqrt{2}-33\)

b) câu b đề sai

16 tháng 7 2017

câu a, \(\left(2-\sqrt{2}\right)\left(-5\sqrt{2}\right)-\left(3\sqrt{2}-5\right)^2=-10\sqrt{2}+5.2-\left(8-30\sqrt{2}+25\right)\)

= \(-33+20\sqrt{2}\)

14 tháng 10 2018

\(2\sqrt{3a}-\sqrt{75a}+a\sqrt{\dfrac{13,5}{2a}}-\dfrac{2}{5}\sqrt{300a^2}\)

\(=2\sqrt{3a}-5\sqrt{3a}+a\sqrt{\dfrac{27a}{\left(2a\right)^2}}-\dfrac{2}{5}\sqrt{100a^2.300}\\ =2\sqrt{a}-5\sqrt{3a}+\dfrac{a.3}{2a}\sqrt{3a}-\dfrac{2}{5}\left|10a\right|\sqrt{3a}\\ =2\sqrt{3a}-5\sqrt{3a}+1,5\sqrt{3a}-4a\sqrt{3a}\\ =-1,5\sqrt{3a}-4a\sqrt{3a}\)

15 tháng 6 2017

minh văn nguyễn

a: \(=-10\sqrt{2}+10-\left(18-2\cdot3\sqrt{2}\cdot5+25\right)\)

\(=-10\sqrt{2}+19-43+30\sqrt{2}\)

\(=-24+20\sqrt{2}\)

b: \(=2\sqrt{3a}-5\sqrt{3a}+a\cdot\sqrt{\dfrac{27}{4a}}-\dfrac{2}{5}\cdot10a\sqrt{3a}\)

\(=-3\sqrt{3a}-4a\sqrt{3a}+\sqrt{\dfrac{27a}{4}}\)

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

\(=\sqrt{3a}\left(-\dfrac{3}{2}-4a\right)\)

2:

\(VT=\dfrac{a^2b}{a-b}\cdot\dfrac{2\sqrt{2}\left(a-b\right)}{5\sqrt{3}\cdot a^2\sqrt{b}}=\dfrac{2}{15}\cdot\sqrt{6b}=VP\)
1: \(=9\sqrt{ab}+\dfrac{7\sqrt{ab}}{b}-\dfrac{5\sqrt{ab}}{a}-3\sqrt{ab}=\)6căn ab+căn ab(7/b-5/a)

=căn ab(6+7/b-5/a)

28 tháng 6 2021

`M=sqrt{(3a-1)^2}+2a-3`

`=|3a-1|+2a-3`

`=3a-1+2a-3(do \ a>=1/3)`

`=5a-4`

`N=sqrt{(4-a)^2}-a+5`

`=|4-a|-a+5`

`=a-4-a+5(do \ a>4)`

`=1`

`I=sqrt{(3-2a)^2}+2-7`

`=|3-2a|-5`

`=3-2a-5(do \ a<3/2)`

`=-2-2a`

`K=(a^2-9)/4*sqrt{4/(a-2)^2}`

`=(a^2-9)/4*|2/(a-2)|`

`=(a^2-9)/(2|a-2|)`

Nếu `3>a>2=>|a-2|=a-2`

`=>K=(a^2-9)/(2(a-2))`

Nếu `a<2=>|a-2|=2-a`

`=>K=(a^2-9)/(2(2-a))`

28 tháng 6 2021

\(M=\left|3a-1\right|+2a-3\)

\(a-\dfrac{1}{3}\ge0\)

\(\Rightarrow M=3a-1+2a-3=5a-4\)

\(N=\left|4-a\right|-a+5\)

\(4-a< 0\)

\(\Rightarrow N=a-4-a+5=1\)

\(I=\left|3-2a\right|-5\)

\(a-\dfrac{3}{2}< 0\)

\(\Rightarrow I=3-2a-5=-2a-2\)

K, Ta có : \(a-3< 0\)

\(\Rightarrow K=\dfrac{2\left(a^2-9\right)}{4\left|a-2\right|}=\dfrac{\left(a-3\right)\left(a+3\right)}{\left|2a-4\right|}\)
 

23 tháng 12 2020

a) Ta có: \(P=\left(\dfrac{1}{\sqrt{x}-\sqrt{x-1}}-\dfrac{x-3}{\sqrt{x-1}-\sqrt{2}}\right)\left(\dfrac{2}{\sqrt{2}-\sqrt{x}}-\dfrac{\sqrt{x}+\sqrt{2}}{\sqrt{2x}-x}\right)\)

\(=\left(\dfrac{\sqrt{x}+\sqrt{x-1}}{x-\left(x-1\right)}-\dfrac{\left(\sqrt{x-1}-\sqrt{2}\right)\left(\sqrt{x-1}+\sqrt{2}\right)}{\sqrt{x-1}-\sqrt{2}}\right)\cdot\left(\dfrac{2}{\sqrt{2}-\sqrt{x}}-\dfrac{\sqrt{x}+\sqrt{2}}{\sqrt{x}\left(\sqrt{2}-\sqrt{x}\right)}\right)\)

\(=\left(\sqrt{x}+\sqrt{x-1}-\sqrt{x-1}-\sqrt{2}\right)\cdot\left(\dfrac{2\sqrt{x}}{\sqrt{x}\left(\sqrt{2}-\sqrt{x}\right)}-\dfrac{\sqrt{x}+\sqrt{2}}{\sqrt{x}\left(\sqrt{2}-\sqrt{x}\right)}\right)\)

\(=\left(\sqrt{x}-\sqrt{2}\right)\cdot\dfrac{2\sqrt{x}-\sqrt{x}-\sqrt{2}}{-\sqrt{x}\left(\sqrt{x}-2\right)}\)

\(=\left(\sqrt{x}-\sqrt{2}\right)\cdot\dfrac{\sqrt{x}-\sqrt{2}}{-\sqrt{x}\left(\sqrt{x}-2\right)}\)

\(=\dfrac{\sqrt{2}-\sqrt{x}}{\sqrt{x}}\)

b) Ta có: \(x=3-2\sqrt{2}\)

\(=2-2\cdot\sqrt{2}\cdot1+1\)

\(=\left(\sqrt{2}-1\right)^2\)

Thay \(x=\left(\sqrt{2}-1\right)^2\) vào biểu thức \(P=\dfrac{\sqrt{2}-\sqrt{x}}{\sqrt{x}}\), ta được: 

\(P=\dfrac{\sqrt{2}-\sqrt{\left(\sqrt{2}-1\right)^2}}{\sqrt{\left(\sqrt{2}-1\right)^2}}\)

\(=\dfrac{\sqrt{2}-\left(\sqrt{2}-1\right)}{\sqrt{2}-1}\)

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

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

\(=\sqrt{2}+1\)

Vậy: Khi \(x=3-2\sqrt{2}\) thì \(P=\sqrt{2}+1\)

23 tháng 12 2020

cái x-3 ở tử phân tích kiểu j ra đc cái kia v bạn

 

a) Ta có: \(A=\dfrac{a^2-1}{3}\cdot\sqrt{\dfrac{9}{\left(1-a\right)^2}}\)

\(=\dfrac{\left(a+1\right)\cdot\left(a-1\right)}{3}\cdot\dfrac{3}{\left|1-a\right|}\)

\(=\dfrac{\left(a+1\right)\left(a-1\right)}{1-a}\)

=-a-1

b) Ta có: \(B=\sqrt{\left(3a-5\right)^2}-2a+4\)

\(=\left|3a-5\right|-2a+4\)

\(=5-3a-2a+4\)

=9-5a

c) Ta có: \(C=4a-3-\sqrt{\left(2a-1\right)^2}\)

\(=4a-3-\left|2a-1\right|\)

\(=4a-3-2a+1\)

\(=2a-2\)

d) Ta có: \(D=\dfrac{a-2}{4}\cdot\sqrt{\dfrac{16a^4}{\left(a-2\right)^2}}\)

\(=\dfrac{a-2}{4}\cdot\dfrac{4a^2}{\left|a-2\right|}\)

\(=\dfrac{a^2\left(a-2\right)}{-\left(a-2\right)}\)

\(=-a^2\)