a) Ta có: \(\dfrac{x-2}{15}+\dfrac{x-3}{14}+\dfrac{x-4}{13}+\dfrac{x-5}{12}=4\)

\(\Leftrightarrow\dfrac{x-2}{15}-1+\dfrac{x-3}{14}-1+\dfrac{x-4}{13}-1+\dfrac{x-5}{12}-1=0\)

\(\Leftrightarrow\dfrac{x-17}{15}+\dfrac{x-17}{14}+\dfrac{x-17}{13}+\dfrac{x-17}{12}=0\)

\(\Leftrightarrow\left(x-17\right)\left(\dfrac{1}{15}+\dfrac{1}{14}+\dfrac{1}{13}+\dfrac{1}{12}\right)=0\)

mà \(\dfrac{1}{15}+\dfrac{1}{14}+\dfrac{1}{13}+\dfrac{1}{12}>0\)

nên x-17=0

hay x=17

Vậy: x=17

b) Ta có: \(\dfrac{x+1}{19}+\dfrac{x+2}{18}+\dfrac{x+3}{17}+...+\dfrac{x+18}{2}+18=0\)

\(\Leftrightarrow\dfrac{x+1}{19}+1+\dfrac{x+2}{18}+1+\dfrac{x+3}{17}+1+...+\dfrac{x+18}{2}+1=0\)

\(\Leftrightarrow\dfrac{x+20}{19}+\dfrac{x+20}{18}+\dfrac{x+20}{17}+...+\dfrac{x+20}{2}=0\)

\(\Leftrightarrow\left(x+20\right)\left(\dfrac{1}{19}+\dfrac{1}{18}+\dfrac{1}{17}+...+\dfrac{1}{2}\right)=0\)

mà \(\dfrac{1}{19}+\dfrac{1}{18}+\dfrac{1}{17}+...+\dfrac{1}{2}>0\)

nên x+20=0

hay x=-20

Vậy: x=-20

(8 x 18 -5 x 18 -18 x3) x y + 2 x y =8 x 7 + 2

<=>144 x y -90 x y -54 x y + 2 x y = 58

<=>2 x y = 58

<=> y = 29

Vậy y = 29

Tìm y biết : 
(8 x 18 - 5 x 18 - 18 x 3) x y + 2 x y = 8 x 7 + 2

                    [ 18 x ( 8 - 5 - 3 ) ] x y = 56 + 2

                    [ 18 x ( 8 - 5 - 3 ) ] x y = 58

                                 ( 18 x 0 ) x y = 58

                                 0 x y + 2 x y = 58

                                            2 x y = 58 

                                                  y = 58 : 2

                                                  y = 29

(8 x 18 - 5 x 18 - 18 x 3) x y + 2 x y

=[(8 - 5- 3) x 18] x y + 2 x y

=[0 x 18] x y + 2 x y

= 0 nhân cho bất kì số nào cũng bằng 0 nên chứng tỏ bài này cho sai đề 

\(\frac{1.5.18+2.10.36+3.15.54}{1.3.9+2.6.18+3.9.27}=\frac{1.5.18.\left(1+2.2.2+3.3.3\right)}{1.3.9.\left(1+2.2.2+3.3.3\right)}\)

\(=\frac{1.5.18}{1.3.9}=\frac{10}{3}\)

a) 32 : 4 : 2 = 8 : 2 = 4 

     32 : 4 : 2 = 32 : 2 = 16 

b) 18 : 2 x 3 = 18 : 6 = 3

     18 : 2 x 3 = 9 x 3 = 18

c: =>x^3+9x^2+27x+27-x^2+6x-9-x^2+6x-9=6x+18

=>x^3+7x^2+39x+9-6x-18=0

=>x^3+7x^2+33x-9=0

=>\(x\simeq0.26\)

d: =>x^3-3x^2+3x-1-x^3-2x^2-x=10x-5x^2-11x-22

=>x^3-5x^2+2x-1=-5x^2-x-22

=>x^3+3x+21=0

=>\(x\simeq2.40\)

Đề câu a có nhầm không nhỉ chứ lớp 8 chưa học phương trình vô tỉ ;-;

Không nhầm tag mình làm tiếp

a, Ta có : \(\left(x+2\right)^3-2\left(x-3\right)^2+18=0\)

\(\Leftrightarrow x^3+12x+6x^2+8-2x^2+12x-18+18=0\)

\(\Leftrightarrow x^3+4x^2+24x+8=0\)

b, Ta có : \(\left(x-5\right)^3-x\left(x-2\right)\left(x+2\right)+125=0\)

\(\Leftrightarrow x^3+75x-15x^2-125-x^3+4x+125=0\)

\(\Leftrightarrow-15x^2+79x=0\)

\(\Leftrightarrow x\left(-15x+79\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{71}{15}\end{matrix}\right.\)

Vậy ...

Câu a xem lại giúp ạ nghiệm rất xấu ;V

`b)(x-5)^3-x(x-2)(x+2)=-125`

`<=>x^3-15x^2+75x-125+125-x(x^2-4)=0`

`<=>x^3-15x^2+75x-x^3+4x^2=0`

`<=>75x-11x^2=0`

`<=>x(75-11x)=0`

`<=>` \(\left[ \begin{array}{l}x=0\\x=\dfrac{75}{11}\end{array} \right.\) 

\(\frac{5.2^{18}.3^{18}.2^{12}-2.2^{28}.3^{14}.3^4}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}=\frac{5.2^{30}.3^{18}-2^{29}.3^{18}}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}=\frac{2^{29}.3^{18}\left(5.2-1\right)}{2^{28}.3^{18}\left(5-7.2\right)}\)

\(\frac{2^{29}.3^{18}.9}{2^{28}.3^{18}.-9}=\frac{2.9}{-9}=-2\)

ko phải tìm x nha

\(1,\left(x+y\right)^2-\left(x-y\right)^2=\left[\left(x+y\right)-\left(x-y\right)\right]\left[\left(x+y\right)+\left(x-y\right)\right]=\left(x+y-x+y\right)\left(x+y+x-y\right)=2y.2x=4xy\)

\(2,\left(x+y\right)^3-\left(x-y\right)^3-2y^3\)

\(=x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3-2y^3\)

\(=6x^2y\)

\(3,\left(x+y\right)^2-2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\\ =\left[\left(x+y\right)-\left(x-y\right)\right]^2\\ =\left(x+y-x+y\right)^2\\ =4y^2\)

\(4,\left(2x+3\right)^2-2\left(2x+3\right)\left(2x+5\right)+\left(2x+5\right)^2\\ =\left[\left(2x+3\right)-\left(2x+5\right)\right]^2\\ =\left(2x+3-2x-5\right)^2\\ =\left(-2\right)^2\\ =4\)

\(5,9^8.2^8-\left(18^4+1\right)\left(18^4-1\right)\\ =18^8-\left[\left(18^4\right)^2-1\right]\\ =18^8-18^8+1\\ =1\)

1: =x^2+2xy+y^2-x^2+2xy-y^2=4xy

2: =x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3-2y^3

=6x^2y

3: =(x+y-x+y)^2=(2y)^2=4y^2

4: =(2x+3-2x-5)^2=(-2)^2=4

5: =18^8-18^8+1=1

      (8 x 18 -5 x 18 -18 x3) x y + 2 x y =8 x 7 + 2

<=>144 x y -90 x y -54 x y + 2 x y = 58

<=>2 x y = 58

<=> y = 29

vậy y = 29

( mình ko chép lại đề bài đâu nha ,giải lun đó)

[18x(8-5-3)]xy+2xy=56+2

(18x0)xy+2xy=58

0xy+2xy=58

2xy=58

  y=58:2=29

tick cho mình nha