`a)(x-6)^2-(x+6)^2=12`

`<=>(x-6-x-6)(x-6+x+6)=12`

`<=>-12.2x=12`

`<=>2x=-1`

`<=>x=-1/2`

Vậy `x=-1/2`

`b)36x^2-12x+1=81`

`<=>(6x-1)^2=81`

`<=>(6x-1-9)(6x-1+9)=0`

`<=>(6x-10)(6x+8)=0`

`<=>(3x-5)(3x+4)=0`

`<=>` \(\left[ \begin{array}{l}x=\dfrac53\\x=-\dfrac43\end{array} \right.\) 

`c)x^2-4x-12=0`

`<=>x^2-6x+2x-12=0`

`<=>x(x-6)+2(x-6)=0`

`<=>(x-6)(x+2)=0`

`<=>` \(\left[ \begin{array}{l}x=-2\\x=6\end{array} \right.\) 

`d)x^2-5x-6=0`

`<=>x^2-6x+x-6=0`

`<=>x(x-6)+x-6=0`

`<=>(x-6)(x+1)=0`

`<=>` \(\left[ \begin{array}{l}x=6\\x=-1\end{array} \right.\) 

\(a,\Leftrightarrow6x-9+4-2x=-3\Leftrightarrow4x=2\Leftrightarrow x=\dfrac{1}{2}\\ b,\Leftrightarrow\left(x-2021\right)\left(x-6\right)=0\Leftrightarrow\left[{}\begin{matrix}x=2021\\x=6\end{matrix}\right.\\ c,\Leftrightarrow\left(2x-3-6x\right)\left(2x-3+6x\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}-3-4x=0\\8x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{3}{4}\\x=\dfrac{3}{8}\end{matrix}\right.\)

\(36x^2-121=0\)

\(x^2=\dfrac{121}{36}\)

\(x=\dfrac{11}{6}\) hoặc \(x=\dfrac{-11}{6}\)

\(36x^2-121=0\)

\(\Leftrightarrow\)\(36x^2=121\)

\(\Leftrightarrow\)\(x^2=\)\(\dfrac{121}{36}\)

\(\Leftrightarrow\)\(x=\)\(\dfrac{11}{6}\)

Lời giải:

a) 

Áp dụng BĐT Bunhiacopxky:

\((y-2x)^2\leq (16y^2+36x^2)(\frac{1}{16}+\frac{1}{9})=9.\frac{25}{144}\)

\(\Rightarrow \frac{-5}{4}\leq y-2x\leq \frac{5}{4}\Rightarrow \frac{15}{4}\leq y-2x+5\leq \frac{25}{4}\)

Vậy $A_{\min}=\frac{15}{4}$ và $A_{\max}=\frac{25}{4}$

b) 

Áp dụng BĐT Bunhiacopxky:

\((2x-y)^2\leq (\frac{x^2}{4}+\frac{y^2}{9})(16+9)=25\)

\(\Rightarrow -5\leq 2x-y\leq 5\Leftrightarrow -7\leq 2x-y-2\leq 3\)

Vậy $B_{min}=-7; B_{\max}=3$

\(36\times\dfrac{2}{3}=\dfrac{72}{3}=24\\ 280\times\dfrac{3}{5}=\dfrac{840}{5}=168\)

\(\dfrac{36\times2}{3}=24;\dfrac{280\times3}{5}=168\)

36×2/3=72/3=24

280×3/5=840/5=168

nhá

Ta có:

Vậy điều kiện để phân thức xác định là x ≠ 0 và x ≠ 1.

a) \(49-7\left(13-x\right)=14\)

\(\Leftrightarrow7\left(13-x\right)=35\)

\(\Leftrightarrow13-x=5\)

\(\Leftrightarrow x=8\)

b) \(5x-25=10\)

\(\Leftrightarrow5x=35\)

\(\Leftrightarrow x=7\)

bạn tự làm tiếp nha!......^^

a) 49 - 7(13 - x) = 14

=> -7(13 - x) = -35

=> 13 - x = 5

=> x = 8

b) 5x - 25 = 10

=> 5x = 35

=> x = 7

c) 14x - 2.49 = 6.7

=> 14x - 98 = 42

=> 14x = 140

=> x = 10

d) 9x + 2.9 = 27

=> 9x + 18 = 27

=> 9x = 9

=> x = 1

e) 10x + 4.5 = 100

=> 10x + 20 = 100

=> 10x = 80

=> x = 8

chúc pn hc tốt!!! 

49 - 7. ( 13 - x ) = 14                                                    9.x + 2.9 = 27

        7. ( 13 - x ) = 49 - 14 = 35                                   9. ( x + 2 ) = 27

               13 - x   = 35 : 7 = 5                                               x + 2  = 27 : 9 = 3

                       x   = 13 - 5                                                            x = 3 - 2

                        x   = 8                                                                    x = 1

5.x - 15 = 10                                                                     10.x + 4.5 = 100

       5.x  = 10 + 15 = 35                                                      10.x + 20 = 100

           x  = 35 : 5                                                                          10.x = 100 - 20 = 80

            x  = 7                                                                                       x = 80 : 10

14 . x - 2 . 49 = 6.7                                                                               x  = 8 .

  14 . x - 98    = 42

          14 . x    = 42 + 98 = 140

                  x    = 140 : 14

                   x    = 10 

\(x\times3,5+2,49=303,49\)

\(\Leftrightarrow x\times3,5=303,49-2,49\)

\(\Leftrightarrow x\times3,5=301\)

\(\Leftrightarrow x=301:3,5\)

\(\Leftrightarrow x=\frac{301}{3,5}\)

Vậy ...