\(B=x^2-x\)

\(B=x^2-2\cdot x\cdot\frac{1}{2}+\left(\frac{1}{2}\right)^2-\left(\frac{1}{2}\right)^2\)

\(B=\left(x-\frac{1}{2}\right)^2-\frac{1}{4}\)

mà \(\left(x-\frac{1}{2}\right)^2\ge0\forall x\)

\(\Rightarrow B\ge\frac{1}{4}\forall x\)

Dấu "=" xảy ra \(\Leftrightarrow x-\frac{1}{2}=0\Leftrightarrow x=\frac{1}{2}\)

Vậy Bmin = 1/4 <=> x = 1/2

P.s : đây là tìm B min

Còn cách nữa tìm Bmax :v

Vì \(x^2\ge0\forall x\)

\(\Rightarrow B\le x\forall x\)

Dấu "=" xảy ra \(\Leftrightarrow x^2=0\Leftrightarrow x=0\)

Vậy Bmax = 0 <=> x = 0

Ta có B= x² - x= \(\left(x^2-2.\frac{1}{2}x+\frac{1}{4}\right)-\frac{1}{4}\) =\(\left(x-\frac{1}{2}\right)^2-\frac{1}{4}\) \(\le\frac{-1}{4}\)( vì \(\left(x-\frac{1}{2}\right)^2\ge0\forall x\inℝ\))

Suy ra B\(\le\frac{-1}{4}\)

Dấu "=" xảy ra <=> \(\left(x-\frac{1}{2}\right)^2=0\) <=>\(x-\frac{1}{2}=0\) <=> \(x=\frac{1}{2}\)

Vậy B max =\(\frac{-1}{4}\Leftrightarrow x=\frac{1}{2}\)

a) \(\left(x+1\right)\left(x-2\right)< 0\Rightarrow\hept{\begin{cases}x+1>0\\x-2< 0\end{cases}}\Rightarrow\hept{\begin{cases}x>-1\\x< 2\end{cases}}\Rightarrow x=\left\{1;0\right\}\)

b) Xét 2 trường hợp

+ TH1: \(\hept{\begin{cases}x-2< 0\\x+\frac{2}{3}< 0\end{cases}\Rightarrow\hept{\begin{cases}x< 2\\x< -\frac{2}{3}\end{cases}}}\)=> \(x< -\frac{2}{3}\)thỏa mãn đề bài

+ TH2: \(\hept{\begin{cases}x-2>0\\x+\frac{2}{3}>0\end{cases}\Rightarrow\hept{\begin{cases}x>2\\x>-\frac{2}{3}\end{cases}}}\)=> x > 2 thỏa mãn đề bài

Vậy \(\orbr{\begin{cases}x< -\frac{2}{3}\\x>2\end{cases}}\)thỏa mãn đề bài

a) \(\left(x+1\right)\left(x-2\right)< 0\)

TH1: \(\hept{\begin{cases}x+1>0\\x-2< 0\end{cases}}\Rightarrow\hept{\begin{cases}x>-1\\x< 2\end{cases}}\)

\(\Rightarrow x\in\left\{0;1\right\}\)

TH2: \(\hept{\begin{cases}x+1< 0\\x-2>0\end{cases}}\Rightarrow\hept{\begin{cases}x< -1\\x>2\end{cases}}\)

=> Không tồn tại x

Vậy: \(x\in\left\{0;1\right\}\)

b) \(\left(x-2\right)\left(x+\frac{2}{3}\right)>0\)

TH1: \(\hept{\begin{cases}x-2>0\\x+\frac{2}{3}>0\end{cases}}\Rightarrow\hept{\begin{cases}x>2\\x>-\frac{2}{3}\end{cases}}\)

\(\Rightarrow x>2\)

TH2: \(\hept{\begin{cases}x-2< 0\\x+\frac{2}{3}< 0\end{cases}}\Rightarrow\hept{\begin{cases}x< 2\\x< -\frac{2}{3}\end{cases}}\)

\(\Rightarrow x< -\frac{2}{3}\)

Vậy: \(x>2\) hoặc \(x< -\frac{2}{3}\)

=> 4x . 2 = 3y . 5

8x = 15y

=> x = 15; y = 8

T.I.C.K GIÚP MK NHÉ!

A)    \(x-\dfrac{2}{3}=\dfrac{4}{5}\\ x=\dfrac{4}{5}+\dfrac{2}{3}\)

           \(x=\dfrac{22}{15}\)

b)\(\dfrac{7}{9}-x=\dfrac{1}{3}\\ x=\dfrac{7}{9}-\dfrac{1}{3}\\ x=\dfrac{4}{9}\)

C)\(x:\dfrac{2}{3}=\dfrac{9}{8}\\ x=\dfrac{9}{8}x\dfrac{2}{3}\\ x=\dfrac{3}{4}\)

\(\orbr{\begin{cases}x-1=4\\x-2=4\end{cases}}\Rightarrow\orbr{\begin{cases}x=4+1\\x=4+2\end{cases}}\Rightarrow\orbr{\begin{cases}x=5\\x=6\end{cases}}\)

Vậy x\(\in\){5;6}

\(\text{Th1: }\hept{\begin{cases}x-1< 0\\x-2\ge0\end{cases}\Rightarrow\hept{\begin{cases}x< 1\\x\ge2\end{cases}\Rightarrow}x\in\varnothing}\)

\(\text{Th2: }\hept{\begin{cases}x-1>0\\x-2\le0\end{cases}\Rightarrow\hept{\begin{cases}x>1\\x\le2\end{cases}\Rightarrow1< x\le}2}\)

\(\text{Khi đó: }\left|x-1\right|+\left|x-2\right|=4\)

\(\Leftrightarrow x-1+2-x=4\)

\(\Leftrightarrow x-x=4-2+1\)

\(\Leftrightarrow0x=3\left(\text{vô lí}\right)\)

Vậy \(x\in\varnothing\)

\(\text{TH3: }\hept{\begin{cases}x-1\ge0\\x-2\ge0\end{cases}\Rightarrow\hept{\begin{cases}x\ge1\\x\ge2\end{cases}\Rightarrow}x\ge1}\)

\(\text{Khi đó: }\left|x-1\right|+\left|x-2\right|=4\)

\(\Leftrightarrow x-1+x-2=4\)

\(\Leftrightarrow2x=7\)

\(\Leftrightarrow x=\frac{7}{2}\left(\text{nhận}\right)\)

\(\text{TH4: }\hept{\begin{cases}x-1\le0\\x-2\le0\end{cases}\Rightarrow\hept{\begin{cases}x\le1\\x\le2\end{cases}\Rightarrow}x\le2}\)

\(\text{Khi đó: }\left|x-1\right|+\left|x-2\right|=4\)

\(\Leftrightarrow1-x+2-x=4\)

\(\Leftrightarrow-2x=1\)

\(\Leftrightarrow x=-\frac{1}{2}\left(\text{nhận}\right)\)

Vậy \(x\in\left\{\frac{-1}{2};\frac{7}{2}\right\}\)

Ta có : \(\frac{5}{7}=\frac{x}{63}\)

\(\Rightarrow\)   \(\frac{45}{63}=\frac{x}{63}\)

\(\Rightarrow\)    \(x=45\)

Vậy x = 45

                       Cbht !!! ❤️❤️❤️ 

\(\frac{5}{7}=\frac{x}{63}\\ \Leftrightarrow5\times63=7x.\)

\(\Leftrightarrow315=7x\)

\(\Leftrightarrow x=45\)

5/7 = x/63

5/7=x:9/63:9

5/7=x:9/7

x=5