a)Đặt \(A=3x^2-x+1\)

          \(A=3\left(x^2-2.\frac{1}{6}x+\frac{1}{36}\right)+\frac{11}{12}\)

            \(A=3\left(x-\frac{1}{6}\right)^2+\frac{11}{12}\)

                   Vì \(3\left(x-\frac{1}{6}\right)^2\ge0\Rightarrow3\left(x-\frac{1}{6}\right)^2+\frac{11}{12}\ge\frac{11}{12}\)

Dấu = xảy ra khi \(x-\frac{1}{6}=0\Rightarrow x=\frac{1}{6}\)

         Vậy Min A = \(\frac{11}{12}\) khi x=1/6

b)Tương tụ

a)\(\frac{x}{6}=\frac{y}{5}\Rightarrow\frac{x+y}{6+5}=\frac{22}{11}=2\)

\(.\frac{x}{6}=2\Rightarrow x=12\)

\(.\frac{y}{5}=2\Rightarrow y=10\)

Vậy......

a) Áp dụng tính chất của dãy tỉ số bằng nhau ta có :

\(\frac{x}{6}=\frac{y}{5}=\frac{x+y}{6+5}=\frac{22}{11}=2\)

\(\Rightarrow\hept{\begin{cases}x=2\times6\\y=2\times5\end{cases}\Rightarrow\hept{\begin{cases}x=12\\y=10\end{cases}}}\)

\(\frac{x}{6}=\frac{y}{5}\)và \(x+y=22\)

ADTC dãy tỉ số bằng nhau ta cs 

\(\frac{x}{6}=\frac{y}{5}=\frac{x+y}{6+5}=\frac{22}{11}=2\)

\(\Rightarrow\hept{\begin{cases}\frac{x}{6}=2\\\frac{y}{5}=2\end{cases}\Rightarrow\hept{\begin{cases}x=12\\x=10\end{cases}}}\)

\(6x=8y\)và \(5x-4y=24\)

Theo bài ra ta cs

\(\frac{x}{8}=\frac{y}{6}\)và \(5x-4y=24\)

ADTC dãy tỉ số bằng nhau ta cs 

\(\frac{x}{8}=\frac{y}{6}=\frac{5x-4y}{5.8-4.6}=\frac{24}{16}=\frac{3}{2}\)

\(\Rightarrow\hept{\begin{cases}\frac{x}{8}=\frac{3}{2}\\\frac{y}{6}=\frac{3}{2}\end{cases}\Rightarrow\hept{\begin{cases}x=12\\y=72\end{cases}}}\)

1.

a,  \(x-14=3x+18\)                                                                       

\(\Rightarrow x-3x=18+14\)                                                                 

\(\Rightarrow-2x=32\Rightarrow x=\frac{32}{-2}=-16\)

b, \(\left(x+7\right).\left(x-9\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x+7=0\\x-9=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-7\\x=9\end{cases}}}\)

c, \(\left|2x-5\right|-7=22\)                                                                     

\(\Rightarrow\left|2x-5\right|=22+7\)

\(\Rightarrow\left|2x-5\right|=29\)

\(\Rightarrow\orbr{\begin{cases}2x+5=29\\2x-5=29\end{cases}}\Rightarrow\orbr{\begin{cases}2x=24\\2x=34\end{cases}\Rightarrow}\orbr{\begin{cases}x=12\\x=17\end{cases}}\)

d,  \(\left(\left|2x\right|-5\right)-7=22\)

\(\Rightarrow\left(\left|2x\right|-5\right)=29\)

\(\Rightarrow\left|2x\right|=29+5\Rightarrow\left|2x\right|=34\Rightarrow x=\pm17\)

e, \(\left|x+3\right|+\left|x+9\right|+\left|x+5\right|=4x\)

Vì \(\left|x+3\right|\ge0;\left|x+9\right|\ge0;\left|x+5\right|\ge0;4x\ge0\)

Nên \(\left|x+3\right|+\left|x+9\right|+\left|x+5\right|=4x\ge0\)

\(\Rightarrow\left|x+3\right|>0\Rightarrow\left|x+3\right|=x+3\)

     \(\left|x+9\right|>0\Rightarrow\left|x+9\right|=x+9\)

      \(\left|x+5\right|>0\Rightarrow\left|x+5\right|=x+5\)

Ta có : 

\(x+3+x+9+x+5=4x\)

\(\Rightarrow3x+\left(3+9+5\right)=4x\)

\(\Rightarrow4x-3x=17\)

\(\Rightarrow x=17\)

2. a , b sai đề bn 

c, \(\left(5x+1\right).\left(y-1\right)=4\)

\(\Rightarrow\left(5x+1\right).\left(y-1\right)\inƯ\left(4\right)\)

\(\text{ }Ư\left(4\right)=\left\{1;-1;2;-2;4;-4\right\}\)

Ta có bảng sau : 

d, \(5xy-5x+y=5\)

\(\Rightarrow\left(5xy-5x\right)+y=5\)

\(\Rightarrow5x.\left(y-1\right)+y=5\)

\(\Rightarrow\left(5x+1\right).\left(y-1\right)=4\)

\(\Rightarrow\left(5x+1\right).\left(y-1\right)\inƯ\left(4\right)\)

\(Ư\left(4\right)=\left\{1;-1;2;-2;4;-4\right\}\)

Ta có bảng sau : 

x - 14 = 3x + 18

x - 3x = 18 + 14

-2x= 32

x= 32 : (-2)

x=-16

`Answer:`

\(3\left(\frac{5}{3}x-7\right)-2\left(1.5x+6\right)-\left(5-x\right)\left(x+4\right)=80+x^2\)

\(\Leftrightarrow3\left(\frac{5x}{3}-7\right)-2\left(5x+6\right)-\left(5-x\right)\left(x+4\right)=80+x^2\)

\(\Leftrightarrow5x-21-10x-12-5x-20+x^2+4x=80+x^2\)

\(\Leftrightarrow5x-21-10x-12-5x-20+4x=80\)

\(\Leftrightarrow-6x-53=80\)

\(\Leftrightarrow-6x=133\)

\(\Leftrightarrow x=-\frac{133}{6}\)

\(\frac{4}{5}x^2\left(\frac{x}{3}-\frac{1}{2}\right)-\left(\frac{1}{5}x-\frac{2}{3}\right)\left(4\frac{x^2}{3}+1\right)=\frac{22}{45}x^2\)

\(\Leftrightarrow36x^2\left(\frac{x}{3}-\frac{1}{2}\right)-45\left(\frac{x}{5}-\frac{2}{3}\right)\left(\frac{4x^2}{3}+1\right)=22x^2\)

\(\Leftrightarrow12x^3-18x^2-12x^3-9x+40x^2+30=22x^2\)

\(\Leftrightarrow22x^2-9x+30=22x^2\)

\(\Leftrightarrow-9x+30=0\)

\(\Leftrightarrow-9x=-30\)

\(\Leftrightarrow x=\frac{10}{3}\)

\(\frac{x+11}{115}+\frac{x+22}{104}=\frac{x+33}{93}+\frac{x+44}{82}\)

\(\Leftrightarrow\frac{1+\left(x+11\right)}{115}+\frac{1+\left(x+22\right)}{104}=\frac{1+\left(x+33\right)}{93}+\frac{1+\left(x+44\right)}{82}\)

\(\Leftrightarrow\frac{x+126}{115}+\frac{x+126}{104}=\frac{x+126}{93}+\frac{x+126}{82}\)

\(\Leftrightarrow\left(x+126\right).\left(\frac{1}{115}+\frac{1}{104}+\frac{1}{93}+\frac{1}{82}\right)=0\)

\(\Leftrightarrow x+126=6\Leftrightarrow x=-126\)vì\(\frac{1}{115}+\frac{1}{104}+\frac{1}{93}+\frac{1}{82}\ne0\)

vậy x=-126

ai trả lời đi

a) Ta có: \(\frac{x+2y}{22}=\frac{x-2y}{14}\Rightarrow\frac{x+2y}{x-2y}=\frac{22}{14}=\frac{11}{7}\)

\(\Rightarrow7\left(x+2y\right)=11\left(x-2y\right)\)

\(\Rightarrow7x+14y=11x-22y\)

\(\Rightarrow14y+22y=11x-7x\)

\(\Rightarrow36y=4x\Rightarrow\frac{x}{y}=\frac{36}{4}=9\)

b) Ta có: \(\frac{x}{y}=9\Rightarrow\frac{x}{9}=\frac{y}{1}\Rightarrow\frac{x^2}{81}=\frac{y^2}{1}\)

Áp dụng tính chất dãy tỉ số bằng nhau, ta có:

\(\frac{x^2}{81}=\frac{y^2}{1}=\frac{x^2+y^2}{81+1}=\frac{82}{82}=1\)

\(\Rightarrow\frac{x^2}{81}=1\Rightarrow x^2=81\Rightarrow\orbr{\begin{cases}x=81\\x=-81\end{cases}}\)

     \(\frac{y^2}{1}=1\Rightarrow y^2=1\Rightarrow\orbr{\begin{cases}y=1\\y=-1\end{cases}}\)

Vậy .................