cái này mà bạn ko biết làm á, bấm máy tính tạch tạch mấy phát là ra mà

lười làm nên nhờ mấy bạn giải dùm

a: TH1: x>=0

=>x+x=1/3

=>x=1/6(nhận)

TH2: x<0

Pt sẽ là -x+x=1/3

=>0=1/3(loại)

b: \(\Leftrightarrow\left\{{}\begin{matrix}x>=0\\x^2-x-2=0\end{matrix}\right.\Leftrightarrow x=2\)

c: \(\Leftrightarrow\dfrac{1}{x-1}-\dfrac{1}{x-3}+\dfrac{1}{x-3}-\dfrac{1}{x-8}+\dfrac{1}{x-8}-\dfrac{1}{x-20}-\dfrac{1}{x-20}=\dfrac{-3}{4}\)

\(\Leftrightarrow\dfrac{1}{x-1}-\dfrac{2}{x-20}=\dfrac{-3}{4}\)

\(\Leftrightarrow\dfrac{x-20-2x+2}{\left(x-1\right)\left(x-20\right)}=\dfrac{-3}{4}\)

\(\Leftrightarrow-3\left(x^2-21x+20\right)=4\left(-x-18\right)\)

\(\Leftrightarrow3x^2-63x+60=4x+72\)

=>3x^2-67x-12=0

hay \(x\in\left\{22.51;-0.18\right\}\)

1)\(B=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{2017}{2018}\)

\(B=\dfrac{1}{2018}\)

2)a)\(x^2-2x-15=0\)

\(\Leftrightarrow x^2-2x+1-16=0\)

\(\Leftrightarrow\left(x-1\right)^2-16=0\)

\(\Leftrightarrow\left(x-5\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-3\end{matrix}\right.\)

3)\(\dfrac{a}{b}=\dfrac{d}{c}\)

\(\Rightarrow\dfrac{a^2}{b^2}=\dfrac{d^2}{c^2}=\dfrac{a}{b}\cdot\dfrac{d}{c}=\dfrac{ad}{bc}\)

Lại có:\(\dfrac{a^2}{b^2}=\dfrac{d^2}{c^2}=\dfrac{a^2+d^2}{b^2+c^2}\)

\(\Rightarrow\dfrac{a^2+d^2}{b^2+c^2}=\dfrac{ad}{bc}\)

4)Ta có:\(g\left(x\right)=-x^{101}+x^{100}-x^{99}+...+x^2-x+1\)

\(g\left(x\right)=-x^{101}+\left(x^{100}-x^{99}+...+x^2-x+1\right)\)

\(g\left(x\right)=-x^{101}+f\left(x\right)\)

\(\Rightarrow f\left(x\right)-g\left(x\right)=f\left(x\right)+x^{101}-f\left(x\right)=x^{101}\)

Tại x=0 thì f(x)-g(x)=0

Tại x=1 thì f(x)-g(x)=1

CHu làm cô liễu ko lo làm Mai báo cô

a)

\(\left|\dfrac{1}{2}-\dfrac{1}{3}+x\right|=-\dfrac{1}{4}-y\\ \Rightarrow\left\{{}\begin{matrix}\dfrac{1}{2}-\dfrac{1}{3}+x=-\dfrac{1}{4}-y\\\dfrac{1}{2}-\dfrac{1}{3}+x=\dfrac{1}{4}+y\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x+y=-\dfrac{5}{12}\\x-y=\dfrac{1}{12}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-\dfrac{1}{6}\\y=-\dfrac{1}{4}\end{matrix}\right.\)

b)\(\left|x-y\right|+\left|y+\dfrac{9}{25}\right|=0\)

ta thấy : \(\left|x-y\right|\ge0\\ \left|y+\dfrac{9}{25}\right|\ge0\)\(\Rightarrow\left|x-y\right|+\left|y+\dfrac{9}{25}\right|\ge0\)

đẳng thửc xảy ra khi : \(\left\{{}\begin{matrix}x-y=0\\y+\dfrac{9}{25}=0\end{matrix}\right.\Rightarrow x=y=-\dfrac{9}{25}\)

vậy \(\left(x;y\right)=\left(-\dfrac{9}{25};-\dfrac{9}{25}\right)\)

c) \(\left(\dfrac{1}{2}x-5\right)^{20}+\left(y^2-\dfrac{1}{4}\right)^{10}=0\)

ta thấy \(\left(\dfrac{1}{2}x-5\right)^{20}\:và\:\left(y^2-\dfrac{1}{4}\right)^{10}\) là các lũy thừa có số mũ chẵn

\(\Rightarrow\:\)\(\left(\dfrac{1}{2}x-5\right)^{20}\ge0\\ \left(y^2-\dfrac{1}{4}\right)^{10}\ge0\)\(\Rightarrow\left(\dfrac{1}{2}x-5\right)^{20}+\left(y^2-\dfrac{1}{4}\right)^{10}\ge0\)

đẳng thức xảy ra khi \(\left\{{}\begin{matrix}\dfrac{1}{2}x-5=0\\y^2-\dfrac{1}{4}=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=10\\\left[{}\begin{matrix}y=-\dfrac{1}{2}\\y=\dfrac{1}{2}\end{matrix}\right.\end{matrix}\right.\)

vậy cặp số x,y cần tìm là \(\left(10;\dfrac{1}{2}\right)\:hoặc\:\left(10;-\dfrac{1}{2}\right)\)

d)

\(\left|x\left(x^2-\dfrac{5}{4}\right)\right|=x\\ \Leftrightarrow x\left(x^2-\dfrac{5}{4}\right)=x\left(vì\:x\ge0\right)\\ \Leftrightarrow x\left(x^2-\dfrac{9}{4}\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x^2-\dfrac{9}{4}=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=\dfrac{3}{2}\end{matrix}\right.\end{matrix}\right.\)

vậy x cần tìm là \(-\dfrac{3}{2};0;\dfrac{3}{2}\)

e)\(x^2+\left(y-\dfrac{1}{10}\right)^4=0\)

ta thấy: \(x^2\ge0;\left(y-\dfrac{1}{10}\right)^4\ge0\)

\(\Rightarrow x^2+\left(y-\dfrac{1}{10}\right)^4\ge0\)

đẳng thức xảy ra khi: \(\left\{{}\begin{matrix}x=0\\y=\dfrac{1}{10}\end{matrix}\right.\)

vậy cặp số cần tìm là \(0;\dfrac{1}{10}\)

Bài 1:

a, \(2y.\left(y-\dfrac{1}{7}\right)=0\)

\(\Rightarrow\left\{{}\begin{matrix}2y=0\\y-\dfrac{1}{7}=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}y=0\\y=\dfrac{1}{7}\end{matrix}\right.\)

Vậy \(y\in\left\{0;\dfrac{1}{7}\right\}\)

b, \(\dfrac{-2}{5}+\dfrac{2}{3}y+\dfrac{1}{6}y=\dfrac{-4}{15}\)

\(\Rightarrow\dfrac{5}{6}y=\dfrac{-4}{15}+\dfrac{2}{5}\)

\(\Rightarrow\dfrac{5}{6}y=\dfrac{2}{15}\)

\(\Rightarrow y=\dfrac{4}{25}\)

Vậy \(y=\dfrac{4}{25}\)

Chúc bạn học tốt!!!

Bài 1:

a, \(2y\left(y-\dfrac{1}{7}\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}2y=0\\y-\dfrac{1}{7}=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}y=0\\y=\dfrac{1}{7}\end{matrix}\right.\)

Vậy...

b, \(\dfrac{-2}{5}+\dfrac{2}{3}y+\dfrac{1}{6}y=\dfrac{-4}{15}\)

\(\Rightarrow\dfrac{5}{6}y=\dfrac{2}{15}\)

\(\Rightarrow y=\dfrac{4}{25}\)

Vậy...

Bài 2:

a, \(x\left(x-\dfrac{4}{7}\right)>0\)

\(\Rightarrow\left\{{}\begin{matrix}x>0\\x-\dfrac{4}{7}>0\end{matrix}\right.\) hoặc \(\left\{{}\begin{matrix}x< 0\\x-\dfrac{4}{7}< 0\end{matrix}\right.\)

\(\Rightarrow x>\dfrac{4}{7}\left(x\ne0\right)\) hoặc \(x< \dfrac{4}{7}\left(x\ne0\right)\)

Vậy...

Các phần còn lại tương tự nhé

1.Tính

a.\(\dfrac{7}{23}\left[(-\dfrac{8}{6})-\dfrac{45}{18}\right]=\dfrac{7}{23}.-\dfrac{12}{6}=-\dfrac{7}{6}\)

b.\(\dfrac{1}{5}\div\dfrac{1}{10}-\dfrac{1}{3}(\dfrac{6}{5}-\dfrac{9}{4})=2-(-\dfrac{7}{20})=\dfrac{47}{20}\)

c.\(\dfrac{3}{5}.(-\dfrac{8}{3})-\dfrac{3}{5}\div(-6)=-\dfrac{3}{2}\)

d.\(\dfrac{1}{2}.(\dfrac{4}{3}+\dfrac{2}{5})-\dfrac{3}{4}.(\dfrac{8}{9}+\dfrac{16}{3})=-\dfrac{19}{5}\)

e.\(\dfrac{6}{7}\div(\dfrac{3}{26}-\dfrac{3}{13})+\dfrac{6}{7}.(\dfrac{1}{10}-\dfrac{8}{5})=-\dfrac{61}{7}\)

Bài 2

a.\(1^2_5x+\dfrac{3}{7}=\dfrac{4}{5}\)

\(x=\dfrac{13}{49}\)

b.\(\left|x-1,5\right|=2\)

Xảy ra 2 trường hợp

TH1

\(x-1,5=2\)

\(x=3,5\)

TH2

\(x-1,5=-2\)

\(x=-0,5\)

Vậy \(x=3,5\) hoặc \(x=-0,5\) .

Ngại làm quá trời ơi,lần sau bn tách ra nhá làm vậy mỏi tay quá.

Ths bn nhé

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

\(x=\dfrac{-2}{5}-\dfrac{3}{10}\)

\(x=\dfrac{-7}{10}\)

b) \(x+\dfrac{5}{6}=\dfrac{2}{5}-\left(-\dfrac{2}{3}\right)\)

\(x+\dfrac{5}{6}=\dfrac{2}{5}+\dfrac{2}{3}\)

\(x+\dfrac{5}{6}=\dfrac{16}{15}\)

\(x=\dfrac{16}{15}-\dfrac{5}{6}\)

\(x=\dfrac{7}{30}\)

c) \(1\dfrac{2}{5}x+\dfrac{3}{7}=-\dfrac{4}{5}\)

\(\dfrac{7}{5}x+\dfrac{3}{7}=-\dfrac{4}{5}\)

\(\dfrac{7}{5}x=-\dfrac{4}{5}-\dfrac{3}{7}\)

\(\dfrac{7}{5}x=\dfrac{-43}{35}\)

\(\Rightarrow x=\dfrac{-43}{49}\)

d) \(\left[x+\dfrac{3}{4}\right]-\dfrac{1}{3}=0\)

\(\left[x+\dfrac{3}{4}\right]=0+\dfrac{1}{3}\)

\(\left[x+\dfrac{3}{4}\right]=\dfrac{1}{3}\)

\(x=\dfrac{1}{3}-\dfrac{3}{4}\)

\(x=\dfrac{-5}{12}\)

e) \(\left[x+\dfrac{4}{5}\right]-\left(-3,75\right)=-\left(-2,15\right)\)

\(\left[x+\dfrac{4}{5}\right]+3,75=2,15\)

\(x+\dfrac{4}{5}=2,15-3,75\)

\(x+\dfrac{4}{5}=-\dfrac{8}{5}\)

\(x=\dfrac{-8}{5}-\dfrac{4}{5}\)

\(x=\dfrac{-12}{5}\)

f) \(\left(x-2\right)^2=1\)

\(\Rightarrow x=1\)

Sức chịu đựng có giới hạn -.-

- Mình tiếp tục cho Nguyễn Phương Trâm nhé.

g, \(\left(2x-1\right)^3=-27\)

\(\Rightarrow\left(2x-1\right)^3=\left(-3\right)^3\)

\(\Rightarrow2x-1=-3\)

\(\Rightarrow2x=-2\)

=> \(x=-1\)

- Vậy x = -1

h,\(\dfrac{x-1}{-15}=-\dfrac{60}{x-1}\)

\(\Rightarrow\left(x-1\right)^2=-60.\left(-15\right)\)

\(\Rightarrow\left(x-1\right)^2=900 \)

\(\Rightarrow\left(x-1\right)^2=30^2\Rightarrow x-1=30\)

=> x = 31

i,\(x:\left(\dfrac{-1}{2}\right)^3=\dfrac{-1}{2}\)

=> \(x:\left(-\dfrac{1}{8}\right)=-\dfrac{1}{2}\)

\(\Rightarrow x=\dfrac{1}{16}\)

- Vậy x=\(\dfrac{1}{16}\)

j, \(\left(\dfrac{3}{4}\right)^5.x=\left(\dfrac{3}{4}\right)^7\)

\(\Rightarrow \left(\dfrac{3}{4}\right).x=\left(\dfrac{3}{4}\right)^2\)

\(\Rightarrow x=\left(\dfrac{3}{4}\right)^2:\dfrac{3}{4}\)

\(\Rightarrow x=\dfrac{3}{4}\)

- Vạy x = \(\dfrac{3}{4}\)

k, \(8^x:2^x=4\Rightarrow\left(8:2\right)^x=4\)

=>\(4^x=4\)

=> x = 1

- Vậy x = 1

a) \(\left[\left(\dfrac{3}{5}\right)^2-\left(\dfrac{2}{5}\right)^2\right]\cdot X=\left(\dfrac{1}{5}\right)^3\)

\(\left(\dfrac{3}{5}-\dfrac{2}{5}\right)\left(\dfrac{3}{5}+\dfrac{2}{5}\right)\cdot X=\dfrac{1}{125}\)

\(\dfrac{1}{5}\cdot1\cdot X=\dfrac{1}{125}\)

\(X=\dfrac{1}{125}:\dfrac{1}{5}=\dfrac{1}{25}\)

b) \(1\dfrac{2}{5}\cdot x+\dfrac{3}{7}=\dfrac{-4}{5}\)

\(1\dfrac{2}{5}\cdot x=\dfrac{-4}{5}-\dfrac{3}{7}\)

\(1\dfrac{2}{5}\cdot x=-\dfrac{43}{35}\)

\(x=-\dfrac{43}{35}:1\dfrac{2}{5}=-\dfrac{43}{49}\)

c) \(\left(3x-2\right)^2=9\)

*Nếu \(9=3^2\) thì:

\(3x-2=3\)

\(3x=5\Rightarrow x=\dfrac{5}{3}\)

*Nếu \(9=\left(-3\right)^2\) thì

\(3x-2=-3\)

\(3x=-1\Rightarrow x=-\dfrac{1}{3}\)

d) \(\left|x+\dfrac{1}{3}\right|-4=-1\)

\(\left|x+\dfrac{1}{3}\right|=3\)

\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{3}=3\\x+\dfrac{1}{3}=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{8}{3}\\x=-\dfrac{10}{3}\end{matrix}\right.\)

Chúc bạn học giỏi.

a)\(\dfrac{3^2-2^2}{5^2}.x=\dfrac{1}{5^3}\)

\(\Leftrightarrow\dfrac{5}{5^2}.x=\dfrac{1}{5^3}\)

\(\Leftrightarrow\dfrac{1}{5}.x=\dfrac{1}{5^3}\)

\(\Leftrightarrow x=\dfrac{1}{25}\)

b)\(\dfrac{7}{5}x+\dfrac{3}{7}=-\dfrac{4}{5}\)

\(\Leftrightarrow\dfrac{7}{5}x=-\dfrac{43}{35}\)

\(\Leftrightarrow x=\dfrac{-43}{49}\)

c)\(9x^2-12x+4=9\)

\(\Leftrightarrow9x^2-12x-5=0\)

\(\Leftrightarrow9x^2-15x+3x-5=0\)

\(\Leftrightarrow3x\left(3x-5\right)+3x-5=0\)

\(\Leftrightarrow\left(3x-5\right)\left(3x+1\right)=0\)

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

d)\(\left|x+\dfrac{1}{3}\right|=3\)

\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{3}=3\\x+\dfrac{1}{3}=-3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{8}{3}\\x=-\dfrac{10}{3}\end{matrix}\right.\)

bài 1)
a) \(\dfrac{11}{13}-\left(\dfrac{5}{42}-x\right)=-\left(\dfrac{15}{28}-\dfrac{11}{15}\right) \)
\(\left(\dfrac{5}{42}-x\right)=\dfrac{11}{13}+\dfrac{15}{28}-\dfrac{11}{15}\)
\(x=\dfrac{5}{42}-\dfrac{3541}{5460}=-\dfrac{413}{780}\)
b) \(\left|x+\dfrac{4}{15}\right|-\left|-3,75\right|=-\left|2,15\right|\)
\(\left|x+\dfrac{4}{15}\right|=-\left|2,15\right|+\left|3,75\right|=1,6\)
\(\Rightarrow x+\dfrac{4}{15}=1,6\) hoặc \(x+\dfrac{4}{15}=-1,6\)
\(\Rightarrow x=\dfrac{4}{3}\) hoặc \(x=-\dfrac{28}{15}\)
c) \(\dfrac{5}{3}-\left|x-\dfrac{3}{2}\right|=-\dfrac{1}{2}\)
\(\Rightarrow\left|x-\dfrac{3}{2}\right|=\dfrac{5}{3}+\dfrac{1}{2}=\dfrac{13}{6}\)
\(\Rightarrow x-\dfrac{3}{2}=\dfrac{13}{6}\) hoặc \(x-\dfrac{3}{2}=-\dfrac{13}{6}\)
\(\Rightarrow x=\dfrac{11}{3}\) hoặc \(x=-\dfrac{2}{3}\)
d)\(\left(x-\dfrac{2}{3}\right).\left(2x-\dfrac{3}{2}\right)=0\)
\(\Rightarrow x-\dfrac{2}{3}=0\) hoặc \(2x-\dfrac{3}{2}=0\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=\dfrac{3}{4}\end{matrix}\right.\)
3) a) \(\left(x^{^2}-4\right)^{^2}+\left(x+2\right)^{^2}=0\)
Vì \(\left(x^{^2}-4\right)^{^2}\ge0,\left(x+2\right)^{^2}\ge0\) nên :
\(\left\{{}\begin{matrix}x^{^2}-4=0\\x+2=0\end{matrix}\right.\Rightarrow x=\pm2\)

b) \(\left(x-y\right)^{^2}+\left|y+2\right|=0\)
Vì \(\left\{{}\begin{matrix}\left(x-y\right)^{^2}\ge0\\\left|y+2\right|\ge0\end{matrix}\right.\) nên \(\left\{{}\begin{matrix}x-y=0\\y+2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x-y=0\\y=-2\end{matrix}\right.\Rightarrow x=-2;y=-2\)
c) \(\left|x-y\right|+\left|y+\dfrac{9}{25}\right|=0\)
Vì \(\left\{{}\begin{matrix}\left|x-y\right|\ge0\\\left|y+\dfrac{9}{25}\right|\ge0\end{matrix}\right.\) nên \(\left\{{}\begin{matrix}x-y=0\\y+\dfrac{9}{25}=0\end{matrix}\right.\Rightarrow y=-\dfrac{9}{25};x=-\dfrac{9}{25}\)
d) \(\left|\dfrac{1}{2}-\dfrac{1}{3}+x\right|=\left(-\dfrac{1}{4}\right)-\left|y\right|\)
\(\Rightarrow\left|\dfrac{1}{2}-\dfrac{1}{3}+x\right|+\left|y\right|=-\dfrac{1}{4}\)
Vì \(\left\{{}\begin{matrix}\left|\dfrac{1}{2}-\dfrac{1}{3}+x\right|\ge0\\\left|y\right|\ge0\end{matrix}\right.\) mà \(\left|\dfrac{1}{2}-\dfrac{1}{3}+x\right|+\left|y\right|=-\dfrac{1}{4}\) nên không tồn tại x,y thỏa mãn đề bài .