1. Đặt $x^2+x=a$ thì pt trở thành:

$a^2+4a=12$
$\Leftrightarrow a^2+4a-12=0$

$\Leftrightarrow  (a-2)(a+6)=0$

$\Leftrightarrow a-2=0$ hoặc $x+6=0$

$\Leftrightarrow x^2+x-2=0$ hoặc $x^2+x+6=0$

Dễ thấy $x^2+x+6=0$ vô nghiệm.

$\Rightarrow x^2+x-2=0$

$\Leftrightarrow (x-1)(x+2)=0$

$\Leftrightarrow x=1$ hoặc $x=-2$

2.

$x(x-1)(x+1)(x+2)=24$
$\Leftrightarrow [x(x+1)][(x-1)(x+2)]=24$

$\Leftrightarrow (x^2+x)(x^2+x-2)=24$

$\Leftrightarrow a(a-2)=24$ (đặt $x^2+x=a$)

$\Leftrightarrow a^2-2a-24=0$

$\Leftrightarrow (a+4)(a-6)=0$

$\Leftrightarrow a+4=0$ hoặc $a-6=0$

$\Leftrightarrow x^2+x+4=0$ hoặc $x^2+x-6=0$

Nếu $x^2+x+4=0$

$\Leftrightarrow (x+\frac{1}{2})^2=\frac{1}{4}-4<0$ (vô lý - loại)

Nếu $x^2+x-6=0$

$\Leftrightarrow (x-2)(x+3)=0$

$\Leftrightarrow x-2=0$ hoặc $x+3=0$
$\Leftrightarrow x=2$ hoặc $x=-3$

3.
$(x-7)(x-5)(x-4)(x-2)=72$

$\Leftrightarrow [(x-7)(x-2)][(x-5)(x-4)]=72$
$\Leftrightarrow (x^2-9x+14)(x^2-9x+20)=72$
$\Leftrightarrow a(a+6)=72$ (đặt $x^2-9x+14=a$)

$\Leftrightarrow a^2+6a-72=0$

$\Leftrightarrow (a-6)(a+12)=0$

$\Leftrightarrow a-6=0$ hoặc $a+12=0$

$\Leftrightarrow x^2-9x+8=0$ hoặc $x^2-9x+26=0$
$\Leftrightarrow x^2-9x+8=0$ (dễ thấy pt $x^2-9x+26=0$ vô nghiệm)

$\Leftrightarrow (x-1)(x-8)=0$

$\Leftrightarrow x-1=0$ hoặc $x-8=0$

$\Leftrightarrow x=1$ hoặc $x=8$

\(a)\left(x^2+x\right)^2+4\left(x^2+x\right)=12\\ \Leftrightarrow\left(x^2+x\right)^2+4\left(x^2+x\right)-12=0\)

Đặt \(t=x^2+x\left(t\ge0\right)\)

\(\Leftrightarrow t^2+4t-12=0\\ \Leftrightarrow\left[{}\begin{matrix}t=2\\t=-6\end{matrix}\right.\)

Với \(t=2\Rightarrow x^2+x=2\Rightarrow x^2-x-2=0\Rightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)

Với \(t=-6\Rightarrow x^2+x=-6\Rightarrow x^2+x+6=0\Rightarrow x\notin\)

Vậy...

Nguyễn TrươngNguyễn Việt LâmNguyenTruong Viet TruongKhôi BùiAkai HarumaÁnh LêDƯƠNG PHAN KHÁNH DƯƠNGPhùng Tuệ Minhsaint suppapong udomkaewkanjana

Unruly KidAkai HarumaNguyễn Thanh HằngLê Anh DuyKhôi BùiNguyễn Việt LâmNguyễn TrươngDũng NguyễnNguyenTRẦN MINH HOÀNG

Bài 1

a) \(5\times72\times10\times2=\left(5\times2\times10\right)\times72=100\times72=7200\) 

b) \(40\times125=5\times\left(8\times125\right)=5\times1000=5000\) 

c) \(16\times6\times25=4\times4\times6\times25=\left(4\times6\right)\times\left(4\times25\right)=24\times100=2400\) Bài 2:

a) \(24\times57+43\times24=24\times\left(57+43\right)=24\times100=2400\) 

b) \(12\times19+80\times12+12=12\times\left(19+80+1\right)=12\times100=1200\) 

c) \(\left(36\times15\times169\right)\div\left(5\times18\times13\right)\) 

 \(=\left(18\times2\times3\times5\times13\times13\right)\div\left(5\times18\times13\right)\) 

\(=\left(2\times3\times13\right)\times\left(18\times5\times13\right)\div\left(5\times18\times13\right)\) 

\(=2\times3\times13\)

\(=78\)

d) \(\left(44\times52\times60\right)\div\left(11\times13\times15\right)\) 

\(=\left(4\times11\times4\times13\times4\times15\right)\div\left(11\times13\times15\right)\)

\(=\left(4\times4\times4\right)\times\left(11\times13\times15\right)\div\left(11\times13\times15\right)\)

\(=4\times4\times4\)

\(=64\)

Bài 3:

a) \(x-280\div35=5\times54\) 

                \(x-8=270\) 

                      \(x=270+8\) 

                      \(x=278\) 

b) \(\left(x-280\right)\div35=54\div4\) 

    \(\left(x-280\right)\div35=\dfrac{27}{2}\) 

               \(x-280=\dfrac{27}{2}\times35\) 

                \(x-280=\dfrac{945}{2}\) 

                          \(x=\dfrac{945}{2}+280\) 

                          \(x=\dfrac{1505}{2}\) 

c) \(\left(x-128+20\right)\div192=0\) 

                 \(x-128+20=0\times192\) 

                \(x-128+20=0\) 

                        \(x-128=0-20\) 

                        \(x-128=-20\)

                                  \(x=-20+128\) 

                                 \(x=108\) 

d) \(4\times\left(x+200\right)=460+85\times4\) 

    \(4\times\left(x+200\right)=460+340\) 

    \(4\times\left(x+200\right)=800\) 

             \(x+200=800\div4\) 

             \(x+200=200\) 

                      \(x=200-200\) 

                      \(x=0\) 

Bài 4:

a) \(\dfrac{7}{12}-\dfrac{5}{12}=\dfrac{2}{12}=\dfrac{1}{6}\) 

b) \(\dfrac{8}{11}+\dfrac{19}{11}=\dfrac{27}{11}\) 

c) \(\dfrac{3}{8}+\dfrac{5}{12}=\dfrac{9}{24}+\dfrac{10}{24}=\dfrac{19}{24}\) 

d) \(\dfrac{3}{4}+\dfrac{7}{12}=\dfrac{9}{12}+\dfrac{7}{12}=\dfrac{16}{12}=\dfrac{4}{3}\) 

Bài 5:

a) \(x-\dfrac{6}{7}=\dfrac{5}{2}\) 

           \(x=\dfrac{5}{2}+\dfrac{6}{7}\) 

           \(x=\dfrac{47}{14}\) 

b) \(\dfrac{12}{7}\div x+\dfrac{2}{3}=\dfrac{7}{5}\) 

            \(\dfrac{12}{7}\div x=\dfrac{7}{5}-\dfrac{2}{3}\) 

             \(\dfrac{12}{7}\div x=\dfrac{11}{15}\) 

                       \(x=\dfrac{12}{7}\div\dfrac{11}{15}\) 

                        \(x=\dfrac{180}{77}\)

`@` `\text {Ans}`

`\downarrow`

`1,`

`a)`

`5 \times 72 \times 10 \times 2`

`= 5 \times 2 \times 10 \times 72`

`= 10 \times 10 \times 72`

`= 100 \times 72`

`= 7200`

`b)`

`40 \times 125`

`= 4 \times 10 \times 25 \times 5`

`= (5 \times 10) \times (4 \times 25)`

`= 50 \times 100`

`= 5000`

`c)`

`4 \times 2021 \times 25`

`= (4 \times 25) \times 2021`

`= 100 \times 2021`

`= 202100`

`d)`

`16 \times 6 \times 25`

`= 4 \times 4 \times 6 \times 25`

`= (4 \times 25) \times 4 \times 6`

`= 100 \times 24`

`= 2400`

`2,`

`a)`

`24 \times 57 + 43 \times 24`

`= 24 \times (57+43)`

`= 24 \times 100`

`= 2400`

`b)`

`12 \times 19 + 80 \times 12 +12`

`= 12 \times (19 + 80 + 1)`

`= 12 \times 100`

`= 1200`

`c)`

`(36 \times 15 \times 169) \div (5 \times 18 \times 13)`

`= 36 \times 15 \times 169 \div 5 \div 18 \div 13`

`= 6 \times 6 \times 3 \times 5 \times 13 \times 13 \div 5 \div 3 \times 6 \div 13`

`= (6 \div 6) \times (3 \div 3) \times (5 \div 5) \times (13 \div 13) \times 6 \times 13`

`= 6 \times 13`

`= 78`

`d)`

`(44 \times 52 \times 60) \div ( 11 \times 13 \times 15)`

`= 44 \times 52 \times 60 \div 11 \div 13 \div 15`

`= 4 \times 11 \times 13 \times 4 \times 15 \times 4 \div 11 \div 13 \div 15`

`= (11 \div 11) \times (13 \div 13) \times (15 \div 15) \times 4 \times 4 \times`

`= 4 \times 4 \times 4`

`= 64`

`3,`

`a)`

`x - 280 \div 35 = 5 \times 54`

`x - 8 = 270`

`x = 270 + 8`

`x = 278`

`b)`

`(x - 280) \div 35 = 54 \div 4`

`(x - 280) \div 35 = 13,5`

`x - 280 = 13,5 \times 35`

`x - 280 = 472,5`

`x = 472,5 + 280`

`x = 752,5`

`c)`

`(x - 128 + 20) \div 192 = 0`

`x - 128 + 20 = 0 \times 192`

`x - 128 + 20 = 0`

`x - 108 = 0`

`x = 0 + 108`

`x = 108`

`d)`

`4 \times (x + 200) = 460 + 85 \times 4`

`4 \times (x+200) = 460 + 340`

`4 \times (x+200) = 800`

`x + 200 = 800 \div 4`

`x + 200 = 200`

`x = 200 - 200`

`x = 0`

`4,`

`a)`

`7/12 - 5/12`

`= (7 - 5)/12`

`= 2/12`

`= 1/6`

`b)`

`8/11 + 19/11`

`= (8+19)/11`

`= 27/11`

`c)`

`3/8 + 5/12`

`= 9/24 + 10/24`

`= 19/24`

`d)`

`3/4 + 7/12`

`= 9/12 + 7/12`

`= 16/12`

`= 4/3`

`5,`

`a)`

`x - 6/7 = 5/2`

`x = 5/2 + 6/7`

`x = 47/14`

`b)`

`12/7 \div x + 2/3 = 7/5`

`12/7 \div x = 7/5 - 2/3`

`12/7 \div x = 11/15`

`x = 12/7 \div 11/15`

`x = 180/77`

`@` `\text {Kaizuu lv uuu}`

mình giải từng bài nhá

hả đơn giản

4.x=16

b​; x(x-1)(x+1)(x+2)-24

=(x²+x)(x²+x-2)-24

​Đ​ặt x²​+x=k khi đ​ó​ k(k-2)-24=k²-2k-24

​=(k²-2k+1)-25=(k-1)²-5²

​ =(k-1-5)(k-1+5)=(k-6)(k+4)

c; (x+2)(x-2)(x²-10)-72

​ =(x²-4)(x²-10)-72

​Đ​ặt x²​-7=k khi đ​ó​ (k-3)(k+3)-72=k²-9-72

=k²-81=(k-9)(k+9)=(x²-7-9)(x²-7+9)

=(x²-16)(x^​2+2)=(x-4)(x+4)(x²+2)

d; (x-7)(x-5)(x-4)(x-2)-72

=(x²-9x+14)(x²-9x+8)-72

Đ​ặt x²-9x​+11=k khi đ​ó​ (k+3)(k-3)-72=k²-9-72

=k²-81=(k-9)(k+9)=(x²-9x+11-9)(x²-9x+11+9)

=(x²-9x+2)(x²-9x+20)

=(x²-9x+2)(x²-4x-5x​+20)

=(x²-9x+2)(x-4)(x-5)