\(\dfrac{x^2-4x-80}{x^2-16}-\dfrac{1}{\sqrt{x}+2}+\dfrac{1}{\sqrt{x}-2}\)

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31 tháng 7 2017

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

\(\Leftrightarrow4\sqrt{x+1}-3\sqrt{x+1}+2\sqrt{x+1}+\sqrt{x+1}=16\)

\(\Leftrightarrow4\sqrt{x+1}=16\)

\(\Leftrightarrow\sqrt{x+1}=4\)

<=> x + 1 = 16

<=> x = 15 (nhận)

~ ~ ~

\(\sqrt{4x+20}-3\sqrt{5+x}+\dfrac{4}{3}\sqrt{9x+45}=6\)

\(\Leftrightarrow2\sqrt{x+5}-3\sqrt{x+5}+4\sqrt{x+5}=6\)

\(\Leftrightarrow3\sqrt{x+5}=6\)

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

<=> x + 5 = 4

<=> x = - 1 (nhận)

31 tháng 7 2017

tính tan40°×tan45°×tan50°
#Help me -.-

9 tháng 8 2017

2. ĐK: \(x\ge0\)

Đặt \(\left\{{}\begin{matrix}a=\sqrt{x}\ge0\\b=\sqrt{x^2+4}\ge0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x=2a^2\\x^2+4=b^2\\3\sqrt{x^3+4x}=3ab\end{matrix}\right.\)

pt trên được viết lại thành

\(2a^2+b^2-3ab=0\)

\(\Leftrightarrow\left(a-b\right)\left(2a-b\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}a=b\\a=\dfrac{1}{2}b\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=\sqrt{x^2+4}\\\sqrt{x}=\dfrac{1}{2}\sqrt{x^2+4}\end{matrix}\right.\)

Đến đây dễ rồi nhé ^^

12 tháng 8 2018

a.\(\sqrt{\left(x-3\right)^2}=3-x\)

\(\Leftrightarrow x-3=3-x\)

\(\Leftrightarrow2x=6\)

\(\Leftrightarrow x=3\)

b.\(\sqrt{4x^2-20x+25}+2x=5\)

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

\(\Leftrightarrow2x-5=5-2x\)

\(\Leftrightarrow4x=10\)

\(\Leftrightarrow x=\dfrac{5}{2}\)

c.

d.\(\sqrt{x^2-\dfrac{1}{2}x+\dfrac{1}{16}}=\dfrac{1}{4}-x\)

\(\Leftrightarrow\sqrt{\left(x-\dfrac{1}{4}\right)^2}=\dfrac{1}{4}-x\)

\(\Leftrightarrow x-\dfrac{1}{4}=\dfrac{1}{4}-x\)

\(\Leftrightarrow x=\dfrac{1}{4}\)

a: =>|x-3|=3-x

=>x-3<=0

hay x<=3

b: =>|2x-5|=-2x+5

=>2x-5<=0

=>x<=5/2

c: =>|căn x-1-1|=căn x-1-1

=>căn x-1-1>=0

=>căn x-1>=1

=>x-1>=1

hay x>=2

2 tháng 7 2018

a) \(\sqrt{\left(x-3\right)^2}=3\Leftrightarrow\left|x-3\right|=3\) \(\Leftrightarrow\left[{}\begin{matrix}x-3=3\\x-3=-3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=6\left(N\right)\\x=0\left(N\right)\end{matrix}\right.\)

b) \(\sqrt{4x^2-20x+25}+2x=5\Leftrightarrow\left|2x-5\right|+2x-5=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-5\ge0\\2x-5+2x-5=0\end{matrix}\right.\\\left\{{}\begin{matrix}2x-5\le0\\5-2x+2x-5=0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge\dfrac{5}{2}\\4x-10=0\end{matrix}\right.\\\left\{{}\begin{matrix}x\le\dfrac{5}{2}\\0x=0\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge\dfrac{5}{2}\\x=\dfrac{10}{4}\left(N\right)\end{matrix}\right.\\x\le\dfrac{5}{2}\end{matrix}\right.\) ** 10/4 = 5/2 rồi**

Kl: x \< 5/2

c) \(\sqrt{1-12x+36x^2}=5\Leftrightarrow\left|1-6x\right|=5\)

\(\Leftrightarrow\left[{}\begin{matrix}1-6x=5\\1-6x=-5\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{2}{3}\left(N\right)\\x=1\left(N\right)\end{matrix}\right.\)

Kl: x=-2/3, x=1

d) Đk: x >/ 1

\(\sqrt{x+2\sqrt{x-1}}=2\Leftrightarrow\left|\sqrt{x-1}+1\right|=2\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-1}+1=2\left(1\right)\\\sqrt{x-1}+2=-2\left(VN\right)\end{matrix}\right.\)

\(\left(1\right)\Leftrightarrow\sqrt{x-1}=1\Leftrightarrow x=2\)(N)

Kl: x=2

e) Đk: x >/ 1

\(\sqrt{x-2\sqrt{x-1}}=\sqrt{x-1}-1\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-1}\ge1\\\left|\sqrt{x-1}-1\right|=\sqrt{x-1}-1\left(1\right)\end{matrix}\right.\)

\(\left(1\right)\Leftrightarrow\sqrt{x-1}-1=\sqrt{x-1}-1\) (luôn đúng)

kl: x >/ 1

f) \(\sqrt{x^2-\dfrac{1}{2}x+\dfrac{1}{16}}=\dfrac{1}{4}-x\) \(\Leftrightarrow\left\{{}\begin{matrix}x\le\dfrac{1}{4}\\\left|\dfrac{1}{4}-x\right|=\dfrac{1}{4}-x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\le\dfrac{1}{4}\\\dfrac{1}{4}-x=\dfrac{1}{4}-x\end{matrix}\right.\)

(luôn đúng)

Kl: x \< 1/4

Lần sau xé nhỏ câu hỏi giùm con nha má, để nhiều thế này thất thu T_T!

14 tháng 9 2017

a)\(\sqrt{\dfrac{4x+3}{x+1}}=3< =>\dfrac{4x+3}{x+1}=3^2=9\)

\(=>4x+3=9\left(x+1\right)=9x+9\)

\(=>4x-9x=9-3< =>-5x=6\)

\(=>x=\dfrac{-6}{5}\)

b)\(\dfrac{1}{2}\sqrt{4x-8}-\dfrac{2}{3}\sqrt{x-2}+\sqrt{\dfrac{x-2}{36}}=7\)

\(< =>\dfrac{1}{2}\sqrt{2^2\left(x-2\right)}-\dfrac{2}{3}\sqrt{x-2}+\sqrt{\dfrac{x-2}{6^2}}=7\)

\(< =>\dfrac{1}{2}.2\sqrt{x-2}-\dfrac{2}{3}\sqrt{x-2}+\dfrac{1}{6}\sqrt{x-2}=7\)

\(< =>\left(1-\dfrac{2}{3}+\dfrac{1}{6}\right)\sqrt{x-2}=7\)

\(< =>\dfrac{1}{2}\sqrt{x-2}=7< =>\sqrt{x-2}=7:\dfrac{1}{2}=14\)

\(< =>x-2=14^2=196< =>x=196+2=198\)

28 tháng 10 2017

\(< =>\sqrt[3]{x+5}=-2\)
<=> \(\left(\sqrt[3]{x+5}\right)^3=-8\)
<=> \(x+5=-8\)
<=> x=-13

11 tháng 8 2018

\(a.\sqrt{1-4a+4a^2}-2a=\sqrt{\left(1-2a\right)^2}-2a=\left|1-2a\right|-2a\)

*\(a>\dfrac{1}{2}\Rightarrow\left|1-2a\right|-2a=2a-1-2a=4a-1\)

* \(a\le\dfrac{1}{2}\Rightarrow\left|1-2a\right|-2a=1-2a-2a=1-4a\)

\(b.x-2y-\sqrt{x^2-4xy+4y^2}=x-2y-\sqrt{\left(x-2y\right)^2}=x-2y-\left|x-2y\right|\)

* \(x\ge2y\Rightarrow x-2y-\left|x-2y\right|=x-2y-x+2y=2x\)

* \(x< 2y\Rightarrow x-2y-\left|x-2y\right|=x-2y-2y+x=2x-4y\)

\(c.x^2+\sqrt{x^4-8x^2+16}=x^2+\sqrt{\left(x^2-4\right)^2}=x^2+\left|x^2-4\right|\)

* \(x^2-4\ge0\Rightarrow x^2+\left|x^2-4\right|=x^2+x^2-4=2x^2-4\)

* \(x^2-4< 0\Rightarrow x^2+\left|x^2-4\right|=x^2+4-x^2=4\)

\(d.2x-1-\dfrac{\sqrt{x^2-10x+25}}{x-5}=2x-1-\dfrac{\sqrt{\left(x-5\right)^2}}{x-5}=2x-1-\dfrac{\left|x-5\right|}{x-5}\)

* \(x\ge5\Rightarrow2x-1-\dfrac{\left|x-5\right|}{x-5}=2x-1-1=2x-2\)

* \(x< 5\Rightarrow2x-1-\dfrac{\left|x-5\right|}{x-5}=2x-1+1=2x\)

\(e.\dfrac{\sqrt{x^4-4x^2+4}}{x^2-2}=\dfrac{\sqrt{\left(x^2-2\right)^2}}{x^2-2}=\dfrac{\left|x^2-2\right|}{x^2-2}\)

* \(x^2\ge2\Rightarrow\dfrac{\left|x^2-2\right|}{x^2-2}=1\)

* \(x^2< 2\Rightarrow\dfrac{\left|x^2-2\right|}{x^2-2}=-1\)

\(f.\sqrt{\left(x-4\right)^2}+\dfrac{x-4}{\sqrt{x^2-8x+16}}=\left|x-4\right|+\dfrac{x-4}{\sqrt{\left(x-4\right)^2}}=\left|x-4\right|+\dfrac{x-4}{\left|x-4\right|}\)

* \(x\ge4\Rightarrow\left|x-4\right|+\dfrac{x-4}{\left|x-4\right|}=x-4+\dfrac{x-4}{x-4}=x-5\)

* \(x< 4\Rightarrow\left|x-4\right|+\dfrac{x-4}{\left|x-4\right|}=4-x-1=5-x\)

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 \(x=\dfrac{144}{25}\)