\(5\sqrt{x-1}-\sqrt{36x-36}\)\(+\sqrt{9x-9}=\sq...">
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12 tháng 9 2020

Ta có: \(5\sqrt{x-1}-\sqrt{36x-36}+\sqrt{9x-9}=\sqrt{8x+12}\)   \(\left(ĐK:x\ge1\right)\)

    \(\Leftrightarrow5\sqrt{x-1}-6\sqrt{x-1}+3\sqrt{x-1}=\sqrt{8x+12}\)

    \(\Leftrightarrow2\sqrt{x-1}=\sqrt{8x+12}\)

    \(\Leftrightarrow\left(2\sqrt{x-1}\right)^2=\left(\sqrt{8x+12}\right)^2\)

    \(\Leftrightarrow4.\left(x-1\right)=8x+12\)

    \(\Leftrightarrow4x-4=8x+12\)

    \(\Leftrightarrow-4x=16\)

    \(\Leftrightarrow x=-4\left(L\right)\)

Vậy \(S=\varnothing\)

12 tháng 9 2020

\(5\sqrt{x-1}-\sqrt{36\left(x-1\right)}+\sqrt{9\left(x-1\right)}=\sqrt{4\left(2x+3\right)}\) 

\(5\sqrt{x-1}-6\sqrt{x-1}+3\sqrt{x-1}=2\sqrt{2x+3}\) 

\(2\sqrt{x-1}=2\sqrt{2x+3}\) 

\(\sqrt{x-1}=\sqrt{2x+3}\) 

\(\hept{\begin{cases}2x+3\ge0\\x-1=2x-3\end{cases}}\) 

\(\hept{\begin{cases}2x\ge-3\\x-2x=-3+1\end{cases}}\) 

\(\hept{\begin{cases}x\ge-\frac{3}{2}\\-x=-2\end{cases}}\) 

\(\hept{\begin{cases}x\ge-\frac{3}{2}\\x=2\end{cases}}\) 

\(\Rightarrow x=2\)

12 tháng 9 2020

a) Ta có: \(\sqrt{4x-8}+5\sqrt{x-2}-\sqrt{9x-18}=20\)       \(\left(ĐK:x\ge2\right)\)

        \(\Leftrightarrow\sqrt{4}.\sqrt{x-2}+5\sqrt{x-2}-\sqrt{9}.\sqrt{x-2}=20\)

        \(\Leftrightarrow2.\sqrt{x-2}+5\sqrt{x-2}-3.\sqrt{x-2}=20\)

        \(\Leftrightarrow4.\sqrt{x-2}=20\)

        \(\Leftrightarrow\sqrt{x-2}=5\)

        \(\Leftrightarrow x-2=25\)

        \(\Leftrightarrow x=27\left(TM\right)\)

Vậy \(S=\left\{27\right\}\)

12 tháng 9 2020

a, PT <=> \(2\sqrt{x-2}+5\sqrt{x-2}-\sqrt{9\left(x-2\right)}=20\)

\(2\sqrt{x-2}+5\sqrt{x-2}-\sqrt{9}\sqrt{x-2}=20\)

\(\left(2+5-3\right)\sqrt{x-2}=20\)

\(4\sqrt{x-2}=20\Leftrightarrow\sqrt{x-2}=5\Leftrightarrow x-2=25\Leftrightarrow x=27\)

26 tháng 7 2016

\(2.< =>5\sqrt{x-1}-6\sqrt{x-1}-3\sqrt{x-1}=2\sqrt{2x-3}\)

\(< =>\sqrt{x-1}\left(5-6+3\right)=2\sqrt{2x-3}\)

\(< =>2\sqrt{x-1}=2\sqrt{2x-3}\)

26 tháng 7 2016

\(< =>x-1=2x-3\)

\(< =>x=2\)

8 tháng 9 2015

2/ \(\Rightarrow5\sqrt{x+1}-6\sqrt{x+1}+3\sqrt{x+1}=2\sqrt{2x+3}\)

\(\Rightarrow\sqrt{x+1}\left(5-6+3\right)=2\sqrt{2x+3}\)

\(\Rightarrow2\sqrt{x+1}=2\sqrt{2x-3}\Rightarrow\sqrt{x+1}=\sqrt{2x+3}\)

\(\Rightarrow x+1=2x+3\Rightarrow x=-2\)

8 tháng 9 2015

bài 1: 

đkxđ: x\(\ge\)0;y\(\ge\)1;z\(\ge\)2

\(\sqrt{x}+\sqrt{y-1}+\sqrt{z-2}=\frac{1}{2}\left(x+y+z\right)\)

\(\Leftrightarrow2\left(\sqrt{x}+\sqrt{y-1}+\sqrt{z-2}\right)=2.\frac{1}{2}\left(x+y+z\right)\)

\(\Leftrightarrow2\sqrt{x}+2\sqrt{y-1}+2\sqrt{z-2}=x+y+z\)

\(\Leftrightarrow x-2\sqrt{x}+y-2\sqrt{y-1}+z-2\sqrt{z-2}=0\)

\(\Leftrightarrow x-2\sqrt{x}+1+y-1-2\sqrt{y-1}+1+z-2-2\sqrt{z-2}+1+1=0\)

\(\Leftrightarrow\left(\sqrt{x}-1\right)^2+\left(\sqrt{y-1}-1\right)^2+\left(\sqrt{z-2}-1\right)^2=-1\)(Vô lí)

Vậy phương trình vô nghiệm

bài 2:

đkxđ: x+1\(\ne\)0

<=>x\(\ne\)-1

\(5\sqrt{x+1}-\sqrt{36x+36}+\sqrt{9x+9}=\sqrt{8x+12}\)

\(\Leftrightarrow5\sqrt{x+1}-\sqrt{36.\left(x+1\right)}+\sqrt{9.\left(x+1\right)}=\sqrt{8x+12}\)

\(\Leftrightarrow5\sqrt{x+1}-6\sqrt{x+1}+3\sqrt{x+1}=\sqrt{8x+12}\)

\(\Leftrightarrow2\sqrt{x+1}=\sqrt{8x+12}\)

\(\Leftrightarrow4.\left(x+1\right)=8x+12\)

\(\Leftrightarrow4x+4=8x+12\)

\(\Leftrightarrow-4x=8\)

\(\Leftrightarrow x=-2\)(thõa mãn)

Vậy x=-2

Bài 1: 

a: \(=\left|5-\sqrt{3}\right|-\left|\sqrt{3}-2\right|\)

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

b; \(B=\dfrac{\left(2-\sqrt{3}\right)\cdot\sqrt{52+30\sqrt{3}}-\left(2+\sqrt{3}\right)\cdot\sqrt{52-30\sqrt{3}}}{\sqrt{2}}\)

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

\(=\dfrac{6\sqrt{3}+10-9-5\sqrt{3}-6\sqrt{3}+10-9+5\sqrt{3}}{\sqrt{2}}\)

\(=\dfrac{20-18}{\sqrt{2}}=\sqrt{2}\)

c: \(C=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{\left(2\sqrt{5}-3\right)^2}}}\)

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

\(=\sqrt{\sqrt{5}-\left(\sqrt{5}-1\right)}=1\)

d: \(A=\left(\sqrt{5}-1\right)\cdot\sqrt{6+2\sqrt{5}}\)

\(=\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)=5-1=4\)

20 tháng 8 2019

\(a,\sqrt{x+1}=\sqrt{2-x}\)

\(\Rightarrow x+1=2-x\)

\(\Rightarrow2x=1\)

\(\Rightarrow x=\frac{1}{2}\)

21 tháng 10 2020

a) \(ĐKXĐ:-1\le x\le2\)

Bình phương 2 vế ta có: 

\(x+1=2-x\)\(\Leftrightarrow2x=1\)\(\Leftrightarrow x=\frac{1}{2}\)( đpcm )

Vậy \(x=\frac{1}{2}\)

b) \(ĐKXĐ:x\ge1\)

\(\sqrt{36x-36}-\sqrt{9x-9}-\sqrt{4x-4}=16-\sqrt{x-1}\)

\(\Leftrightarrow\sqrt{36\left(x-1\right)}-\sqrt{9\left(x-1\right)}-\sqrt{4\left(x-1\right)}+\sqrt{x-1}=16\)

\(\Leftrightarrow6\sqrt{x-1}-3\sqrt{x-1}-2\sqrt{x-1}+\sqrt{x-1}=16\)

\(\Leftrightarrow2\sqrt{x-1}=16\)\(\Leftrightarrow\sqrt{x-1}=8\)

\(\Leftrightarrow x-1=64\)\(\Leftrightarrow x=65\)( thỏa mãn ĐKXĐ )

Vậy \(x=65\)

c) \(ĐKXĐ:x\ge1\)

\(\sqrt{16x-16}-\sqrt{9x-9}+\sqrt{4x-4}+\sqrt{x-1}=8\)

\(\Leftrightarrow\sqrt{16\left(x-1\right)}-\sqrt{9\left(x-1\right)}+\sqrt{4\left(x-1\right)}+\sqrt{x-1}=8\)

\(\Leftrightarrow4\sqrt{x-1}-3\sqrt{x-1}+2\sqrt{x-1}+\sqrt{x-1}=8\)

\(\Leftrightarrow4\sqrt{x-1}=8\)\(\Leftrightarrow\sqrt{x-1}=2\)

\(\Leftrightarrow x-1=4\)\(\Leftrightarrow x=5\)( thỏa mãn ĐKXĐ )

Vậy \(x=5\)

15 tháng 8 2016

\(\sqrt{36x-36}-\sqrt{9x-9}-\sqrt{4x-4}=16-\sqrt{x-1}\)

\(\sqrt{36\left(x-1\right)}-\sqrt{9\left(x-1\right)}-\sqrt{4\left(x-1\right)}=16-\sqrt{x-1}\)

\(6\sqrt{x-1}-3\sqrt{x-1}-2\sqrt{x-1}+\sqrt{x-1}=16\)

\(\sqrt{x-1}\left(6-3-2+1\right)=16\)

\(2\sqrt{x-1}=16\)

\(\sqrt{x-1}=8\)

\(\left(\sqrt{x-1}\right)^2=8^2\)

\(x-1=64\)

\(x=64+1=65\)

15 tháng 8 2016

\(\sqrt{36x-36}-\sqrt{9x-9}-\sqrt{4x-4}=16-\sqrt{x-1}\)ĐK x lớn hơn hoặc bằng 1

\(6\sqrt{x-1}-3\sqrt{x-1}-2\sqrt{x-1}+\sqrt{x-1}=16\)

\(2\sqrt{x-1}=16\)

\(\sqrt{x-1}=8\)

\(x-1=64\)

\(x=65\)thỏa mãn

21 tháng 12 2016

Nếu bạn tinh mắt một chút sẽ thấy:

Câu a: \(5\sqrt{2x-1}+2\sqrt{2x-1}-3\sqrt{x}=6\sqrt{2x-1}-2\sqrt{x}\)

Tương đương \(\sqrt{2x-1}=\sqrt{x}\Leftrightarrow\hept{\begin{cases}2x-1=x\\x\ge0\end{cases}}\Leftrightarrow x=1\).

Câu b: \(2\sqrt{x-5}-\sqrt{x-5}=\sqrt{1-x}\).

Tương đương \(\sqrt{x-5}=\sqrt{1-x}\Leftrightarrow\hept{\begin{cases}x\le1\\x-5=1-x\end{cases}}\) (vô nghiệm)

Câu c: \(\sqrt{\left(x+3\right)\left(x-3\right)}-2\sqrt{x-3}=0\)

Tương đương \(\orbr{\begin{cases}x-3=0\\\sqrt{x+3}-2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=1\end{cases}}\)

21 tháng 12 2016

Ấy chết! Sai ngu ở pt c rồi. Không có nghiệm \(x=1\) nha bạn.

6 tháng 9 2017

2, \(\dfrac{1}{2}\sqrt{x+1}-\dfrac{3}{2}\sqrt{9x+9}+24\sqrt{\dfrac{x+1}{64}}=-17\)

\(\Leftrightarrow\dfrac{1}{2}\sqrt{x+1}-\dfrac{9}{2}\sqrt{x+1}+3\sqrt{x+1}=-17\)

\(\Leftrightarrow-\sqrt{x+1}=-17\)

\(\Leftrightarrow x+1=289\left(x>0\right)\)

\(\Leftrightarrow x=288\)

Vậy x = 288

3, \(-5x+7\sqrt{x}+12=0\)

\(\Leftrightarrow-5x+12\sqrt{x}-5\sqrt{x}+12=0\)

\(\Leftrightarrow\sqrt{x}\left(12-5\sqrt{x}\right)+\left(12-5\sqrt{x}\right)=0\)

\(\Leftrightarrow\left(\sqrt{x}+1\right)\left(12-5\sqrt{x}\right)=0\)

Do \(\sqrt{x}+1>0\)

\(\Rightarrow12-5\sqrt{x}=0\Leftrightarrow x=\dfrac{144}{25}\)

Vậy...

6 tháng 9 2017

1. (Đề có chút sai sai nên mình sửa lại nhé) \(\sqrt{36x-36}-\sqrt{9x-9}-\sqrt{4x-4}=16-\sqrt{x-1}\)

(ĐK: \(x\ge1\))

\(\Leftrightarrow\sqrt{36\left(x-1\right)}-\sqrt{9\left(x-1\right)}-\sqrt{4\left(x-1\right)}=16-\sqrt{x-1}\)

\(\Leftrightarrow6\sqrt{x-1}-3\sqrt{x-1}-2\sqrt{x-1}+\sqrt{x-1}=16\)

\(\Leftrightarrow2\sqrt{x-1}=16\)

\(\Leftrightarrow\sqrt{x-1}=8\)

\(\Leftrightarrow x-1=64\)

\(\Leftrightarrow x=65\left(tm\right)\)

Vậy pt đã cho có nghiệm x=65.

2. \(\dfrac{1}{2}\sqrt{x+1}-\dfrac{3}{2}\sqrt{9x+9}+24\sqrt{\dfrac{x+1}{64}}=-17\)

(ĐK: \(x\ge-1\))

\(\Leftrightarrow\dfrac{1}{2}\sqrt{x+1}-\dfrac{3}{2}\sqrt{9\left(x+1\right)}+3\sqrt{x+1}=-17\)

\(\Leftrightarrow\dfrac{1}{2}\sqrt{x+1}-\dfrac{9}{2}\sqrt{x+1}+3\sqrt{x+1}=-17\)

\(\Leftrightarrow-\sqrt{x+1}=-17\)

\(\Leftrightarrow\sqrt{x+1}=17\)

\(\Leftrightarrow x+1=289\)

\(\Leftrightarrow x=288\left(tm\right)\)

Vậy \(S=\left\{288\right\}\)

3. \(-5x+7\sqrt{x}+12=0\) (ĐK: \(x\ge0\))

\(\Leftrightarrow5x-7\sqrt{x}-12=0\)

\(\Leftrightarrow5x+5\sqrt{x}-12\sqrt{x}-12=0\)

\(\Leftrightarrow5\sqrt{x}\left(\sqrt{x}+1\right)-12\left(\sqrt{x}+1\right)=0\)

\(\Leftrightarrow\left(\sqrt{x}+1\right)\left(5\sqrt{x}-12\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}+1=0\\5\sqrt{x}-12=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=-1\left(vô.lý\right)\\5\sqrt{x}=12\end{matrix}\right.\Leftrightarrow\sqrt{x}=\dfrac{12}{5}\Leftrightarrow x=\dfrac{144}{25}\left(tm\right)\)

Vậy pt có nghiệm \(x=\dfrac{144}{25}\)