1.

$x(x+2)(x+4)(x+6)+8$

$=x(x+6)(x+2)(x+4)+8=(x^2+6x)(x^2+6x+8)+8$

$=a(a+8)+8$ (đặt $x^2+6x=a$)

$=a^2+8a+8=(a+4)^2-8=(x^2+6x+4)^2-8\geq -8$

Vậy $A_{\min}=-8$ khi $x^2+6x+4=0\Leftrightarrow x=-3\pm \sqrt{5}$

2.

$B=5+(1-x)(x+2)(x+3)(x+6)=5-(x-1)(x+6)(x+2)(x+3)$

$=5-(x^2+5x-6)(x^2+5x+6)$

$=5-[(x^2+5x)^2-6^2]$

$=41-(x^2+5x)^2\leq 41$

Vậy $B_{\max}=41$. Giá trị này đạt tại $x^2+5x=0\Leftrightarrow x=0$ hoặc $x=-5$

3.

Đặt $x+3=a; 7-x=b$ thì $a+b=10$ 

$C=a^4+b^4$

Áp dụng BĐT Bunhiacopxky:

$(a^4+b^4)(1+1)\geq (a^2+b^2)^2$

$\Rightarrow C\geq \frac{(a^2+b^2)^2}{2}$
$(a^2+b^2)(1+1)\geq (a+b)^2=100$

$\Rightarrow a^2+b^2\geq 50$

$\Rightarrow C\geq \frac{50^2}{2}=1250$

Vậy $C_{\min}=1250$

Giá trị này đạt tại $a=b=5\Leftrightarrow x=2$

\(\frac{4}{\frac{2}{5}}:\left(-\frac{33}{10}\right)+x=-\frac{1}{\frac{5}{6}}\)

\(10:\left(-\frac{33}{10}\right)+x=-\frac{6}{5}\)

\(-\frac{100}{33}+x=-\frac{6}{5}\)

\(x=\frac{302}{165}\)

1).( 27,56 x 35 ) + ( 27,56 x 67 ) - ( 27,56 x 2)

= (964 + 1846,52) - 55,12

=2810,52 - 55,12

= 2755,4

2).( 4x 35 ) x ( 25 x 5 ) x 2

= ( 140 x 125 ) x2

= 17500 x 2

=35000

4). 3/10

5). 1188

6).  61/6

1)2756   2)35000   3)0   4)3/10   5)10/1/6

1,2755,4

2,35000

3,0

4,\(\frac{3}{10}\)

5,1188

6,\(\frac{61}{6}\)

\(A=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{99}}\)

\(\Rightarrow\dfrac{A}{3}=\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{100}}\)

\(\Rightarrow A-\dfrac{A}{3}=\dfrac{2A}{3}=\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{99}}\right)-\left(\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{100}}\right)\)

\(\Rightarrow\dfrac{2A}{3}=\left(\dfrac{1}{3^2}-\dfrac{1}{3^2}\right)+\left(\dfrac{1}{3^3}-\dfrac{1}{3^3}\right)+...+\left(\dfrac{1}{3^{99}}-\dfrac{1}{3^{99}}\right)+\left(\dfrac{1}{3}-\dfrac{1}{3^{100}}\right)=\dfrac{1}{3}-\dfrac{1}{3^{100}}\)

\(\Rightarrow2A=3\cdot\left(\dfrac{1}{3}-\dfrac{1}{3^{100}}\right)\)

\(\Rightarrow\text{A}=\dfrac{1-\dfrac{1}{3^{99}}}{2}\)

\(\Rightarrow A=\dfrac{1}{2}-\dfrac{1}{2.3^{99}}< \dfrac{1}{2}\)

1, \(x=-\dfrac{7}{3}-\dfrac{1}{3}=-\dfrac{8}{3}\)

2, \(x=\dfrac{1}{8}-\dfrac{3}{8}=-\dfrac{2}{8}=-\dfrac{1}{4}\)

3, \(x=\dfrac{6}{5}+\dfrac{4}{5}=\dfrac{10}{5}=2\)

4, \(x=\dfrac{7}{3}-\dfrac{2}{3}=\dfrac{5}{3}\)

5, \(x+\dfrac{7}{3}=\dfrac{5}{3}\Leftrightarrow x=\dfrac{5}{3}-\dfrac{7}{3}=-\dfrac{2}{3}\)

\(=x+\dfrac{1}{3}=\dfrac{-7}{3}\Leftrightarrow x=\dfrac{-8}{3}\)

\(=\dfrac{1}{8}-x=\dfrac{3}{8}\Leftrightarrow x=\dfrac{-1}{4}\)

\(=x-\dfrac{4}{5}=\dfrac{6}{5}\Leftrightarrow x=2\)

\(=\dfrac{2}{3}+x=\dfrac{7}{3}\Leftrightarrow x=\dfrac{5}{3}\)

\(=x-\dfrac{-7}{3}=\dfrac{5}{3}\Leftrightarrow x=\dfrac{-2}{3}\)

1)x=-7/3-1/3

   x=-8/3

2)x=1/8-3/8

   x=-1/4

3)x=6/5+4/5

   x=2

4)x=7/3-2/3

   x=5/3

5)x=5/3+(-7/3)

   x=-2/3

         Bài 4:

Mỗi ki-lô-gam gạo có giá tiền là: 

          45 000 :  5 = 9 000 (đồng)

Số tiền mua gạo bạn An phải trả là:

         9000 x 20 = 180 000 (đồng)

Số ki-lô-gam gạo bạn Bình mua là:

        20 + 5 = 25 (kg)

Số tiền mua gạo bạn Bình cần trả là:

      9 000  x 25 = 225 000 (đồng)

Đáp số:...

Bài 3 :

\(3\left(đôi.gà\right)=3x2=6\left(con\right)\)

Số phân số số đàn gà tuần này là :

\(1-\dfrac{2}{3}=\dfrac{1}{3}\left(đàn.gà\right)\)

Số phân số số đàn gà còn lại là :

\(1-\dfrac{2}{3}-\dfrac{3}{4}x\dfrac{1}{3}=1-\dfrac{2}{3}-\dfrac{1}{4}=\dfrac{1}{12}\left(đàn.gà\right)\)

Đàn gà có tất cả là :

\(6:\dfrac{1}{12}=6x12=72\left(con\right)\)

Đáp số...

Bài 5 :

1 quyển vở có giá là :

\(14000-12000=2000\left(đồng\right)\)

1 quyển sách có giá là :

\(\left(12000-2000\right):2=5000\left(đồng\right)\)

Đáp số...

\(6-2\left(x-1\right)=4\)

\(\Rightarrow2\left(x-1\right)=6-4\)

\(\Rightarrow2\left(x-1\right)=2\)

\(\Rightarrow x-1=1\)

\(\Rightarrow x=1+1=2\)

________________

\(2\cdot\left(x-2\right)+1=7\)

\(\Rightarrow2\cdot\left(x-2\right)=7-1\)

\(\Rightarrow2\cdot\left(x-2\right)=6\)

\(\Rightarrow x-2=3\)

\(\Rightarrow x=3+2=5\)

_______________

\(\left(2\cdot x-3\right)+4=9\)

\(\Rightarrow2\cdot x-3=5\)

\(\Rightarrow2\cdot x=3+5\)

\(\Rightarrow2\cdot x=8\)

\(\Rightarrow x=\dfrac{8}{2}=4\)

________________

\(\left(3\cdot x-2\right)-1=3\)

\(\Rightarrow3\cdot x-2=3+1\)

\(\Rightarrow3\cdot x-2=4\)

\(\Rightarrow3\cdot x=6\)

\(\Rightarrow x=\dfrac{6}{3}=2\)

a: =>2(x-1)=2

=>x-1=1

=>x=2

b: =>2(x-2)=6

=>x-2=3

=>x=5

c; =>2x-3=5

=>2x=8

=>x=4

d: =>3x-2=4

=>3x=6

=>x=2

e: =>2(6-x)=4

=>6-x=2

=>x=4

f: =>x-2=5

=>x=7

g: =>10-2x=4

=>2x=6

=>x=3

h: =>2x+4=3

=>2x=-1

=>x=-1/2

j: =>x+2=12

=>x=10

l: =>2x+3=3

=>2x=0

=>x=0

\(6-2\left(x-1\right)=4\\ 2\left(x-1\right)=6-4=2\\ x-1=\dfrac{2}{2}=1\\ x=1+1=2\)

\(2\left(6-x\right)+1=5\\ 2\left(6-x\right)=5-1=4\\ 6-x=\dfrac{4}{2}=2\\ x=6-2=4\)

\(\left(4+2x\right)-1=8\\ 3\left(4+2x\right)=8+1=9\\ 4+2x=\dfrac{9}{3}=3\\ 2x=3-4=-1\\ x=-\dfrac{1}{2}\)

\(2\left(x-2\right)+1=7\\ 2\left(x-2\right)=7-1=6\\ x-2=\dfrac{6}{2}=3\\ x=3+2=5\)

\(20+\left(x-2\right)=25\\ x-2=25-20=5\\ x=5+2=7\)

\(\left(x+2\right)-5=7\\ x+2=7+5=12\\ x=12-2=10\)

\(\left(2x-3\right)+4=9\\ 2x-3=9-4=5\\ 2x=5+3=8\\ x=\dfrac{8}{2}=4\)

\(\left(10-\dfrac{2}{x}\right)-1=3\\ 10-\dfrac{2}{x}=3+1=4\\ \dfrac{2}{x}=10-4=6\\ x=\dfrac{2}{6}=\dfrac{1}{3}\)

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

\(\left(3x-2\right)-1=3\\ 3x-2=3+1=4\\ 3x=4+2=6\\ x=\dfrac{6}{3}=2\)

a: =>x=-7/6+5/8=-13/24

b: =>x=-14/25-3/4=-131/100

c: \(x=\dfrac{-33}{26}:\dfrac{-9}{13}=\dfrac{33}{26}\cdot\dfrac{13}{9}=\dfrac{11}{3}\cdot\dfrac{1}{2}=\dfrac{11}{6}\)

d: \(x=\dfrac{4}{9}:\dfrac{5}{3}=\dfrac{4}{9}\cdot\dfrac{3}{5}=\dfrac{12}{45}=\dfrac{4}{15}\)

a, x= 29/10

b, x=9/20

c, x= 10/7

d, x=10/7

e, x= 8/3

a) x=29/10

b) x=9/20

c) x=10/7

d) 10/7

e) 8/3

a)   \(x+\frac{3}{5}=\frac{7}{2}\Leftrightarrow x=\frac{7}{2}-\frac{3}{5}\Leftrightarrow x=\frac{29}{10}\)

b)   \(x-\frac{1}{4}=\frac{1}{5}\Leftrightarrow x=\frac{1}{5}+\frac{1}{4}\Leftrightarrow x=\frac{9}{20}\)

c)   \(2-x=\frac{4}{7}\Leftrightarrow x=2-\frac{4}{7}\Leftrightarrow x=\frac{10}{7}\)

d)   \(x.\frac{2}{5}=\frac{4}{7}\Leftrightarrow x=\frac{4}{7}:\frac{2}{5}\Leftrightarrow x=\frac{10}{7}\)

e)   \(x:\frac{6}{11}=\frac{44}{9}\Leftrightarrow x=\frac{44}{9}.\frac{6}{11}\Leftrightarrow x=\frac{8}{3}\)

1/ \(1+\frac{2}{x-1}+\frac{1}{x+3}=\frac{x^2+2x-7}{x^2+2x-3}\)

ĐKXĐ: \(\hept{\begin{cases}x-1\ne0\\x+3\ne0\end{cases}}\Leftrightarrow\hept{\begin{cases}x\ne1\\x\ne-3\end{cases}}\)

<=> \(1+\frac{2\left(x+3\right)+x-1}{\left(x-1\right)\left(x+3\right)}=\frac{x^2+2x-3-5}{x^2+2x-3}\)

<=> \(1+\frac{2x+6+x-1}{x^2+2x-3}=1-\frac{5}{x^2+2x-3}\)

<=> \(\frac{3x+5}{x^2+2x-3}+\frac{5}{x^2+2x-3}=1-1\)

<=> \(\frac{3x+5}{x^2+2x-3}+\frac{5}{x^2+2x-3}=0\)

<=> \(\frac{3x+10}{x^2+2x-3}=0\)

<=> \(3x+10=0\)

<=> \(x=-\frac{10}{3}\)