a/ \(\left(x-1\right)\left(y+2\right)=7\)

\(\Leftrightarrow x-1;y+2\inƯ\left(7\right)\)

Suy ra :

\(\hept{\begin{cases}x-1=1\\y+2=7\end{cases}}\)  \(\Leftrightarrow\hept{\begin{cases}x=1\\y=5\end{cases}}\)

\(\hept{\begin{cases}x-1=7\\y+2=1\end{cases}}\) \(\Leftrightarrow\hept{\begin{cases}x=8\\y=-1\end{cases}}\)

\(\hept{\begin{cases}x-1=-1\\y+2=-7\end{cases}}\) \(\Leftrightarrow\hept{\begin{cases}x=0\\y=-9\end{cases}}\)

\(\hept{\begin{cases}x-1=-7\\y+2=-1\end{cases}}\) \(\Leftrightarrow\hept{\begin{cases}x=-6\\x=-3\end{cases}}\)

Vậy ......

b/ \(x\left(y-3\right)=-12\)

\(\Leftrightarrow x;y-3\inƯ\left(-12\right)\)

Suy ra :

\(\hept{\begin{cases}x=1\\y-3=-12\end{cases}}\) \(\Leftrightarrow\hept{\begin{cases}x=1\\y=-9\end{cases}}\)

\(\hept{\begin{cases}x=-12\\y-3=1\end{cases}}\) \(\Leftrightarrow\hept{\begin{cases}x=-12\\y=4\end{cases}}\)

\(\hept{\begin{cases}x=-1\\y-3=12\end{cases}}\) \(\Leftrightarrow\hept{\begin{cases}x=-1\\y=15\end{cases}}\)

\(\hept{\begin{cases}x=12\\y-3=-1\end{cases}}\) \(\Leftrightarrow\hept{\begin{cases}x=12\\y=2\end{cases}}\)

Vậy ..

a)Ta xét: có 7 là số nguyên tố => 7= 1.7 = 7.1

\(\orbr{\begin{cases}\hept{\begin{cases}x-1=1\\y+2=7\end{cases}}\\\hept{\begin{cases}x-1=7\\y+2=1\end{cases}}\end{cases}}\Leftrightarrow\orbr{\begin{cases}\hept{\begin{cases}x=2\\y=5\end{cases}}\\\hept{\begin{cases}x=8\\y=-1\end{cases}}\end{cases}}\)\(\orbr{\begin{cases}\hept{\begin{cases}x-1=1\\y+2=7\end{cases}}\\\hept{\begin{cases}x-1=7\\y+2=1\end{cases}}\end{cases}}\Leftrightarrow\)\(\hept{\begin{cases}x-1=7\\y+2=1\end{cases}}\)hay \(\hept{\begin{cases}x-1=1\\y+2=7\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}x=8\\y=-1\end{cases}}\) hay \(\hept{\begin{cases}x=2\\y=5\end{cases}}\)

b)x(y-3)=-12

Ta có: -12=1.(-12)=2.(-6)=3.(-4)=4.(-3)=(-6).2=(-12).1

Bạn xét nghiệm theo từng cặp giá trị tương ứng (12 cặp) sẽ tìm được nghiệm

c) tương tự câu b

làm tiếp :

c/ (x-3)(y-3)=9

=> x-3 ; y-3 thuộc Ư(9)={-1,-3,-9,1,3,9}

Ta có bảng :

Vậy ...

a) \(\sqrt{4x^2+4x+1}=6\)

\(\Leftrightarrow\sqrt{\left(2x+1\right)^2}=6\)

\(\Leftrightarrow\left(2x+1\right)^2=6^2\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+1=6\\2x+1=-6\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-\dfrac{7}{2}\end{matrix}\right.\)

b) \(\sqrt{4x^2-4\sqrt{7}x+7}=\sqrt{7}\)

\(\Leftrightarrow\sqrt{\left(2x-\sqrt{7}\right)^2}=\sqrt{7}\)

\(\Leftrightarrow\left(2x-\sqrt{7}\right)^2=\left(\sqrt{7}\right)^2\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-\sqrt{7}=\sqrt{7}\\2x-\sqrt{7}=-\sqrt[]{7}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{7}\\x=0\end{matrix}\right.\)

a) \(\sqrt{4x^2+4x+1}=6\)

\(\Leftrightarrow\sqrt{\left(2x+1\right)^2}=6\)

\(\Leftrightarrow\left|2x+1\right|=6\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+1=6\\2x+1=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-\dfrac{7}{2}\end{matrix}\right.\)

b) \(pt\Leftrightarrow\sqrt{\left(2x-\sqrt{7}\right)^2}=\sqrt{7}\)

\(\Leftrightarrow\left|2x-\sqrt{7}\right|=\sqrt{7}\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-\sqrt{7}=\sqrt{7}\\2x-\sqrt{7}=-\sqrt{7}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{7}\\x=0\end{matrix}\right.\)

c) \(PT\Leftrightarrow\sqrt{\left(x+\sqrt{3}\right)^2}=2\sqrt{3}\)

\(\Leftrightarrow\left|x+\sqrt{3}\right|=2\sqrt{3}\)

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

d) \(pt\Leftrightarrow\left|x-3\right|=9\Leftrightarrow\left[{}\begin{matrix}x-3=-9\\x-3=9\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-6\\x=12\end{matrix}\right.\)

tớ chỉ làm được phần a)thôi

ta có:\(\left(x-\frac{2}{3}\right):\frac{-3}{7}=\frac{-9}{11}\)

\(x-\frac{2}{3}=\frac{-9}{11}.\frac{-3}{7}\)

\(x-\frac{2}{3}=\frac{27}{77}\)

\(x=\frac{27}{77}+\frac{2}{3}\)

\(x=\frac{235}{231}\)

vậy x=\(\frac{235}{231}\)

a) \(\left(x-\frac{2}{3}\right)\):\(\frac{-3}{7}\)=\(\frac{-9}{1}\)

                        \(x-\frac{2}{3}\)=\(-9\cdot\frac{-3}{7}\)

                        \(x-\frac{2}{3}\)= \(\frac{27}{7}\)

                                     \(x\)= \(\frac{27}{7}\)\(+\frac{2}{3}\)

                                      \(x\)=\(\frac{95}{21}\)

b)\(x:2+x:\frac{5}{2}+x:\frac{1}{3}=\frac{-18}{25}\)

      \(x:\left(2+\frac{5}{2}+\frac{1}{3}\right)=\frac{-18}{25}\)

            \(x:\frac{12+15+2}{6}=\frac{-18}{25}\)

                                \(x:\frac{29}{6}=\frac{-18}{25}\)

                                          \(x=\frac{-18}{25}\cdot\frac{29}{6}\)

                                           \(x=\frac{-87}{25}\)

Lời giải:

a. ĐKXĐ: $x\geq -9$

PT $\Leftrightarrow x+9=7^2=49$

$\Leftrightarrow x=40$ (tm)

b. ĐKXĐ: $x\geq \frac{-3}{2}$

PT $\Leftrightarrow 4\sqrt{2x+3}-\sqrt{4(2x+3)}+\frac{1}{3}\sqrt{9(2x+3)}=15$

$\Leftrightarrow 4\sqrt{2x+3}-2\sqrt{2x+3}+\sqrt{2x+3}=15$

$\Leftrgihtarrow 3\sqrt{2x+3}=15$

$\Leftrightarrow \sqrt{2x+3}=5$

$\Leftrightarrow 2x+3=25$

$\Leftrightarrow x=11$ (tm)

c.

PT \(\Leftrightarrow \left\{\begin{matrix} 2x+1\geq 0\\ x^2-6x+9=(2x+1)^2\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\geq \frac{-1}{2}\\ 3x^2+10x-8=0\end{matrix}\right.\)

\(\Leftrightarrow \left\{\begin{matrix} x\geq \frac{-1}{2}\\ (3x-2)(x+4)=0\end{matrix}\right.\)

\(\Leftrightarrow x=\frac{2}{3}\)

d. ĐKXĐ: $x\geq 1$

PT \(\Leftrightarrow \sqrt{(x-1)+4\sqrt{x-1}+4}-\sqrt{(x-1)+6\sqrt{x-1}+9}=9\)

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

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

\(\Leftrightarrow -1=9\) (vô lý)

Vậy pt vô nghiệm.

a) \(\sqrt{x+9}=7\left(x\ge-9\right)\Rightarrow x+9=49\Rightarrow x=40\)

b) \(4\sqrt{2x+3}-\sqrt{8x+12}+\dfrac{1}{3}\sqrt{18x+27}=15\left(x\ge-\dfrac{3}{2}\right)\)

\(\Rightarrow4\sqrt{2x+3}-\sqrt{4\left(2x+3\right)}+\dfrac{1}{3}\sqrt{9\left(2x+3\right)}=15\)

\(\Rightarrow4\sqrt{2x+3}-2\sqrt{2x+3}+\sqrt{2x+3}=15\)

\(\Rightarrow3\sqrt{2x+3}=15\Rightarrow\sqrt{2x+3}=5\Rightarrow2x+3=25\Rightarrow x=11\)

c) \(\sqrt{x^2-6x+9}=2x+1\)

Vì \(VT\ge0\Rightarrow VP\ge0\Rightarrow x\ge-\dfrac{1}{2}\)

\(\Rightarrow\sqrt{\left(x-3\right)^2}=2x+1\Rightarrow\left|x-3\right|=2x+1\Rightarrow\left[{}\begin{matrix}x-3=2x+1\\x-3=-2x-1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=-4\left(l\right)\\x=\dfrac{2}{3}\end{matrix}\right.\)

d) \(\sqrt{x+3+4\sqrt{x-1}}-\sqrt{x+8+6\sqrt{x-1}}=9\left(x\ge1\right)\)

\(\Rightarrow\sqrt{x-1+4\sqrt{x-1}+4}-\sqrt{x-1+6\sqrt{x-1}+9}=9\)

\(\Rightarrow\sqrt{\left(\sqrt{x-1}+2\right)^2}-\sqrt{\left(\sqrt{x-1}+3\right)^2}=9\)

\(\Rightarrow\left|\sqrt{x-1}+2\right|-\left|\sqrt{x-1}+3\right|=9\)

\(\Rightarrow\sqrt{x-1}+2-\sqrt{x-1}-3=9\Rightarrow-1=9\) (vô lý)

a.\(2x^2+5x+8+\sqrt{x}=x^2+3x+35+x^2+2x-7\)

\(=2x^2+5x+8+\sqrt{x}=2x^2+5x+28\Leftrightarrow\sqrt{x}=20\Leftrightarrow x=400.\)

b.\(3\sqrt{x}+7x+5=\sqrt{x}+4x-6+3x+18\)

\(=3\sqrt{x}+7x+5=\sqrt{x}+7x+12\Leftrightarrow2\sqrt{x}=7\Leftrightarrow x=\frac{49}{4}.\)

c.\(8\sqrt{x}+2x-9=5x+7+6\sqrt{x}-3x-12.\)

\(=8\sqrt{x}+2x-9=2x+6\sqrt{x}-5\Leftrightarrow2\sqrt{x}=4\Leftrightarrow x=4.\)

d.\(2\sqrt{3x}+11x-18=5x+3+6\sqrt{3x}+6x-21\)

\(=2\sqrt{3x}+11x-18=11x+6\sqrt{3x}-19\Leftrightarrow4\sqrt{3x}=1\)

\(\Leftrightarrow\sqrt{3x}=\frac{1}{4}\Leftrightarrow3x=\frac{1}{16}\Leftrightarrow x=\frac{1}{48}.\)

a) \(2x^2+5x+8+\sqrt{x}=x^2+3x+35+x^2+2x-7\)

<=> \(2x^2+5x+8+\sqrt{x}=2x^2+5x+28\)

<=> \(2x^2+5x+8+\sqrt{x}-\left(2x^2+5\right)=28\)

<=> \(\sqrt{x}+8=28\)

<=> \(\sqrt{x}=28-8\)

<=> \(\sqrt{x}=20\)

<=> \(\left(\sqrt{x}\right)^2=20^2\)

<=> x = 400

=> x = 400

b) \(3\sqrt{x}+7x+5=\sqrt{x}+4x-6+3x+18\)

<=> \(3\sqrt{x}+7x+5=7x+\sqrt{x}+12\)

<=> \(3\sqrt{x}+5=7x+\sqrt{x}+12-7x\)

<=> \(3\sqrt{x}+5=\sqrt{x}+12\)

<=> \(3\sqrt{x}=\sqrt{x}+12-5\)

<=> \(3\sqrt{x}=\sqrt{x}+7\)

<=> \(3\sqrt{x}-\sqrt{x}=7\)

<=> \(2\sqrt{x}=7\)

<=> \(\sqrt{x}=\frac{7}{2}\)

<=> \(\left(\sqrt{x}\right)^2=\left(\frac{7}{2}\right)^2\)

<=> \(x=\frac{49}{4}\)

=> \(x=\frac{49}{4}\)

c) \(8\sqrt{x}+2x-9=5x+7+6\sqrt{x}-3x-12\)

<=> \(8\sqrt{x}+2x-9=2x+6\sqrt{x}-5\)

<=> \(8\sqrt{x}-9=2x+6\sqrt{x}-5-2x\)

<=> \(8\sqrt{x}-9=6\sqrt{x}-5\)

<=> \(8\sqrt{x}=6\sqrt{x}-5+9\)

<=> \(8\sqrt{x}=6\sqrt{x}+4\)

<=> \(8\sqrt{x}-6\sqrt{x}=4\)

<=> \(2\sqrt{x}=4\)

<=> \(\sqrt{x}=2\)

<=> \(\left(\sqrt{x}\right)^2=2^2\)

<=> x = 4

=> x = 4

d) \(2\sqrt{3x}+11x-18=5x+3+6\sqrt{3x}+6x-21\)

<=> \(2\sqrt{3x}+11x-18=11x+6\sqrt{3x}-18\)

<=> \(2\sqrt{3x}+11x-18-\left(11x-18\right)=6\sqrt{3x}\)

<=>\(2\sqrt{3x}=6\sqrt{3x}\)

<=> \(2\sqrt{3x}-6\sqrt{3x}=0\)

<=>\(-4\sqrt{3x}=0\)

<=> \(\sqrt{3x}=0\)

<=> \(\left(\sqrt{3x}\right)^2=0^2\)

<=> 3x = 0

<=> x = 0

=> x = 0

a) \(\frac{2}{5}+x=\frac{3}{4}\)

\(x=\frac{3}{4}-\frac{2}{5}\)

\(x=\frac{15}{20}-\frac{8}{20}\)

\(x=\frac{7}{20}\)

\(\)b)

\(x-\frac{1}{15}=\frac{3}{10}\\ x=\frac{3}{10}+\frac{1}{15}\\ x=\frac{9}{30}+\frac{2}{30}\\ x=\frac{11}{30}\)

c)

\(\frac{9}{8}-x=\frac{5}{12}\\ x=\frac{9}{8}-\frac{5}{12}\\ x=\frac{27}{24}-\frac{10}{24}\\ x=\frac{17}{24}\)

d)

\(\frac{3}{5}+x=\frac{5}{4}+\frac{7}{10}\\ \frac{3}{5}+x=\frac{25}{20}+\frac{14}{20}\\\frac{3}{5}+x=\frac{39}{20}\\ x=\frac{39}{20}-\frac{3}{5}\\ x=\frac{39}{20}-\frac{12}{20}\\ x=\frac{27}{20} \)

e)

\(\frac{9}{8}-x=\frac{3}{20}+\frac{2}{5}\\ \frac{9}{8}-x=\frac{3}{20}+\frac{8}{20}\\ \frac{9}{8}-x=\frac{11}{20}\\ x=\frac{9}{8}-\frac{11}{20}\\ x=\frac{45}{40}-\frac{22}{40}\\ x=\frac{23}{40}\)

g)

\(x+\frac{1}{3}=\frac{5}{6}+1\frac{7}{10}\\ x+\frac{1}{3}=\frac{5}{6}+\frac{17}{10}\\ x+\frac{1}{3}=\frac{25}{30}+\frac{51}{30}\\ x+\frac{1}{3}=\frac{76}{30}=\frac{38}{15}\\ x=\frac{38}{15}-\frac{1}{3}\\ x=\frac{38}{15}-\frac{5}{15}\\ x=\frac{33}{15}=\frac{11}{5}\)

h)

\(3x-\frac{3}{5}=\frac{1}{2}\\ 3x=\frac{1}{2}+\frac{3}{5}\\ 3x=\frac{5}{10}+\frac{6}{10}\\ 3x=\frac{11}{10}\\ x=\frac{11}{10}:3\\ x=\frac{11}{10}\cdot\frac{1}{3}\\ x=\frac{11}{30}\)

i)

\(4x+\frac{5}{12}+\frac{4}{9}=1\frac{13}{18}\\ 4x+\frac{5}{12}+\frac{4}{9}=\frac{31}{18}\\ 4x+\frac{5}{12}=\frac{31}{18}-\frac{4}{9}\\ 4x+\frac{5}{12}=\frac{31}{18}-\frac{8}{18}\\ 4x+\frac{5}{12}=\frac{23}{18}\\ 4x=\frac{23}{18}-\frac{5}{12}\\ 4x=\frac{46}{36}-\frac{15}{36}\\ 4x=\frac{31}{36}\\ x=\frac{31}{36}:4\\ x=\frac{31}{36}\cdot\frac{1}{4}\\ x=\frac{31}{144}\)

k)

\(2-\left(3x+\frac{3}{7}\right)=\frac{9}{21}\\ 2-\left(3x+\frac{3}{7}\right)=\frac{3}{7}\\3x+\frac{3}{7}=2-\frac{3}{7}\\ 3x+\frac{3}{7}=\frac{14}{7}-\frac{3}{7}\\ 3x+\frac{3}{7}=\frac{11}{7}\\ 3x=\frac{11}{7}-\frac{3}{7}\\ 3x=\frac{8}{7}\\ x=\frac{8}{7}:3\\ x=\frac{8}{7}\cdot\frac{1}{3}\\ x=\frac{8}{21} \)

αi nhanh mình sẽ Tick ạ.

A = \(\dfrac{3^{100}.\left(-2\right)+3^{101}}{\left(-3\right)^{101}-3^{100}}\) 

A = \(\dfrac{3^{100}.\left(-2\right)+3^{100}.3}{\left(-3\right)^{100}.\left(-3\right)-3^{100}}\)

A = \(\dfrac{3^{100}.\left(-2+3\right)}{3^{100}.\left(-3\right)-3^{100}}\)

A = \(\dfrac{3^{100}.1}{3^{100}.\left(-3-1\right)}\)

A = \(\dfrac{3^{100}}{3^{100}}\) . \(\dfrac{1}{-4}\)

A = - \(\dfrac{1}{4}\)

1/4

9-25=(7-x)-(25+7)

-16=7-x-32

7-x-32=16

7-x=-16+32

7-x=16 

x=16+7

x=23

B,35-3.|x|=5.(2^3-4)

35-3.x=5.(8-4)

35-3.x=5.4

35-3.x=20

3.x=35-20

3.x=15

X=15:3

x =5

C, -6x=18

-6.x=18

X=18:(-6)

X= -3

D,10+2.|x|=2.(3^2-1)

10+2.x=2.8

10+2.x=16

2.x=16-10

2.x =6

X=6:2

x=3

Ok k mk nha 

a) 9 - 25 = ( 7 - x) - (25+7)

    - 16 =  7-x - 32

    7 - x - 32 = -16

   7 - x = -16 + 32

   7 - x = 16

      x = 16 + 7

      x = 23

b) -6x = 18

   - 6 .x = 18

        x = 18 : (-6)

       x = -3

1) 5.( x - 6 ) - 2.( x + 9 ) = 21

           5x - 30 - 2x - 18 = 21

                        3x - 48 = 21

                               3x = 21 + 48

                               3x = 69

                                 x = 23

2) 2.( x + 3 ) + 3.( x +  1 ) = 15 - ( - 9 )

               2x + 6 + 3x + 3 = 24

                            5x + 9 = 24

                                  5x = 24 - 9 

                                  5x = 15

                                   x = 3

3) ( - x + 5 ).(3 - x ) = 0

=> - x + 5 = 0 hoặc 3 - x = 0

=> x = 5 hoặc x = 3

4) ( x - 12 ) - 15 = ( 20 - 7 ) - ( 18 + x )

        x - 12 - 15 = 13 - 18 - x 

               x - 27 = - 5 - x 

                x + x = - 5 + 27

                     2x = 22

                       x = 11

5) x - ( 17 - 8 ) = 5 + ( 10 - 3x )

               x - 9 = 5 + 10 - 3x

            x + 3x = 15 + 9

                  4x = 24

                    x = 6