Bài 3: 

a: =>x=13-24=-11

b: =>3x=12

hay x=4

Bài 2:

a) \(\left(x-3\right)^3+27=0\)

\(\Leftrightarrow\left(x-3\right)^3=0-27\)

\(\Leftrightarrow\left(x-3\right)^3=-27\)

\(\Leftrightarrow\left(x-3\right)^3=\left(-3\right)^3\)

\(\Leftrightarrow x-3=-3\)

\(\Leftrightarrow x=\left(-3\right)+3\)

\(\Leftrightarrow x=0\)

b) \(-125-\left(x+1\right)^3=0\)

\(\Leftrightarrow\left(x+1\right)^3=-125-0\)

\(\Leftrightarrow\left(x+1\right)^3=-125\)

\(\Leftrightarrow\left(x+1\right)^3=\left(-5\right)^3\)

\(\Leftrightarrow x+1=-5\)

\(\Leftrightarrow x=\left(-5\right)-1\)

\(\Leftrightarrow x=-6\)

c) \(\left(2x-\dfrac{1}{4}\right)^2-\dfrac{1}{16}=0\)

\(\Leftrightarrow\left(2x-\dfrac{1}{4}\right)^2=0+\dfrac{1}{16}\)

\(\Leftrightarrow\left(2x-\dfrac{1}{4}\right)^2=\dfrac{1}{16}\)

\(\Leftrightarrow\left(2x-\dfrac{1}{4}\right)^2=\left(\dfrac{1}{4}\right)^2\)

\(\Leftrightarrow2x-\dfrac{1}{4}=\dfrac{1}{4}\)

\(\Leftrightarrow2x=\dfrac{1}{4}+\dfrac{1}{4}\)

\(\Leftrightarrow2x=\dfrac{1}{2}\)

\(\Leftrightarrow x=\dfrac{1}{2}:2\)

\(\Leftrightarrow x=\dfrac{1}{4}\)

d) \(2^x+2^{x+1}=24\)

\(\Leftrightarrow2^x+2^x.2=24\)

\(\Leftrightarrow2^x\left(1+2\right)=24\)

\(\Leftrightarrow2^x.3=24\)

\(\Leftrightarrow2^x=24:3\)

\(\Leftrightarrow2^x=8\)

\(\Leftrightarrow2^x=2^3\)

\(\Rightarrow x=3\)

e) \(\left|x+\dfrac{1}{5}\right|-\dfrac{1}{2}=1\)

\(\Leftrightarrow\left|x+\dfrac{1}{5}\right|=1+\dfrac{1}{2}\)

\(\Leftrightarrow\left|x+\dfrac{1}{5}\right|=\dfrac{3}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{5}=-\dfrac{3}{2}\\x+\dfrac{1}{5}=\dfrac{3}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{17}{10}\\x=\dfrac{13}{10}\end{matrix}\right.\)

g) \(\left|x-3\right|+2x=10\)

\(\Leftrightarrow\left|x-3\right|=10-2x\)

\(\Leftrightarrow\left|x-3\right|=2.5-2x\)

\(\Leftrightarrow\left|x-3\right|=2\left(5-x\right)\)

(không chắc có nên làm tiếp câu g không, thấy đề cứ là lạ, có j sai sai...)

Bài 1:

a) \(2^7+2^9⋮10\)

Ta có: \(2^7+2^9=2^{4.1}.2^3+2^{4.2}.2\)

\(\Leftrightarrow\overline{A6}.2^3+\overline{B6}.2\)

\(\Leftrightarrow\overline{A6}.8+\overline{B6}.2\)

\(\Leftrightarrow\overline{C8}+\overline{D2}\)

\(\Leftrightarrow\overline{E0}\)

Mà \(\overline{E0}⋮10\) \(\Rightarrow2^7+2^9⋮10\)

b) \(8^{24}.25^{10}⋮2^{36}.5^{20}\)

Ta có: \(8^{24}.25^{10}=\left(2^3\right)^{24}.\left(5^2\right)^{10}\)

\(\Leftrightarrow2^{72}.5^{20}\)

Do \(2^{72}⋮2^{36}\) và \(5^{20}⋮5^{20}\) \(\Rightarrow8^{24}.25^{10}⋮2^{36}.5^{20}\)

c) \(3^{10}+3^{12}⋮30\)

Ta có: \(3^{10}+3^{12}=3^{4.2}.3^2+3^{4.3}\)

\(\Leftrightarrow\overline{A1}.3^2+\overline{B1}\)

\(\Leftrightarrow\overline{A1}.9+\overline{B1}\)

\(\Leftrightarrow\overline{C9}+\overline{B1}\)

\(\Leftrightarrow\overline{D0}⋮10\)

(Chứng minh chia hết cho 10 rồi chứng minh chia hết cho 3, mình chưa tìm được cách làm, chờ chút)

\(a,2^7+2^9=2^6\cdot2+2^6\cdot2^3=2^6\cdot\left(2+2^3\right)=2^6\cdot\left(2+8\right)=2^6\cdot10⋮10\)

Vậy \(2^7+2^9⋮10\)

\(b,2^{36}\cdot5^{20}=2^{3\cdot12}\cdot5^{2\cdot10}=\left(2^3\right)^{12}\cdot\left(5^2\right)^{10}=8^{12}\cdot25^{10}\\ \text{Vì }8^{24}⋮8^{12}\text{ và }25^{10}⋮25^{10}\text{ nên }8^{24}\cdot25^{10}⋮8^{12}\cdot25^{10}\text{ hay }8^{24}\cdot25^{10}⋮2^{36}\cdot5^{20}\)

Vậy \(8^{24}\cdot25^{10}⋮8^{12}\cdot25^{10}\)

\(c,3^{10}+3^{12}=3^9\cdot3+3^9\cdot3^3=3^9\cdot\left(3+3^3\right)=3^9\cdot\left(3+27\right)=3^9\cdot30⋮30\)

Vậy \(3^{10}+3^{12}⋮30\)

a; \(x\) - \(\dfrac{3}{5}\) = 1 - \(\dfrac{4}{5}\) + \(\dfrac{1}{6}\)

    \(x\) - \(\dfrac{3}{5}\) = \(\dfrac{30}{30}\) - \(\dfrac{24}{30}\) + \(\dfrac{5}{30}\)

    \(x\) - \(\dfrac{3}{5}\) = \(\dfrac{6}{30}\) + \(\dfrac{5}{30}\)

    \(x\) - \(\dfrac{3}{5}\) =  \(\dfrac{11}{30}\)

   \(x\)        = \(\dfrac{11}{30}\) + \(\dfrac{3}{5}\)

   \(x\)        = \(\dfrac{11}{30}\) + \(\dfrac{18}{30}\)

    \(x\)      = \(\dfrac{29}{30}\)

Vậy \(x\) = \(\dfrac{29}{30}\) 

b; (- \(\dfrac{10}{4}\)) + \(\dfrac{1}{4}\) = \(\dfrac{3}{4}\) thế \(x\) của em đâu nhỉ???

c; - \(\dfrac{3}{2}\) + (\(x\) - \(\dfrac{1}{2}\)) = \(\dfrac{1}{2}\)

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

             \(x\)  - \(\dfrac{1}{2}\) = 2

             \(x\)        = 2 + \(\dfrac{1}{2}\)

             \(x\)       =   \(\dfrac{4}{2}\) + \(\dfrac{1}{2}\)

             \(x\)       = \(\dfrac{5}{2}\)

Vậy \(x=\dfrac{5}{2}\)

d; \(x\) - \(\dfrac{2}{7}\) = \(\dfrac{7}{21}\)

    \(x\)       = \(\dfrac{7}{21}\) + \(\dfrac{2}{7}\)

     \(x\)     =  \(\dfrac{7}{21}\) + \(\dfrac{6}{21}\)

     \(x\)     = \(\dfrac{13}{21}\)

Vậy \(x=\dfrac{13}{21}\)

a) \(x^3\)+\(x^2\)=36

\(\Leftrightarrow\)\(x^3\)+\(x^2\)\(-36=0\)

\(\Leftrightarrow\)\(x^3\)\(-3x^2\)\(+4x^2\)\(-12x\)\(+12x-36=0\)

\(\Leftrightarrow\)\(x^2\left(x-3\right)+4x\left(x-3\right)+12\left(x-3\right)=0\)

\(\Leftrightarrow\)\(\left(x-3\right)\left(x^2+4x+12\right)=0\)

Suy ra: \(x-3=0\) hoặc \(x^2+4x+12=0\)

Vậy \(x=3\)

giờ mình đi học mai sẽ làm nốt phần còn lại

C) \(\left(x^2-5x\right)^2+10\left(x^2-5x\right)+24=0\)

\(\Leftrightarrow\) \(\left(\left(x^2-5x\right)^2+2.\left(x^2-5x\right).5+25\right)-1=0\)

\(\Leftrightarrow\) \(\left(x^2-5x+5\right)^2-1=0\)

\(\Leftrightarrow\) \(\left(x^2-5x+5-1\right).\left(x^2-5x+5+1\right)=0\)

\(\Leftrightarrow\) \(\left(x^2-5x+4\right).\left(x^2-5x+6\right)=0\)

Suy ra \(x^2-5x+4=0\) hoặc \(x^2-5x+6=0\)

Nếu \(x^2-5x+4=0\) \(\Leftrightarrow\) \(\left(x-1\right).\left(x-4\right)=0\) \(\Leftrightarrow\) \(\left[\begin{array}{} x=1\\ x=4 \end{array} \right.\)

Nếu \(x^2-5x+6=0\) \(\Leftrightarrow\) \(\left(x-2\right).\left(x-3\right)=0\) \(\Leftrightarrow\) \(\left[\begin{array}{} x=2\\ x=3 \end{array} \right.\)

Vậy x \(\in\) {1;2;3;4}

Câu a bạn Nguyễn Thị Anh đã trả lời, mình trả lời câu c.

b) Câu này bạn ghi sai đề rồi!

c) Ta có: x/3 = y/4 => x/15 = y/20

                 y/5 = z/7 => y/20 = z/28

=> x/15 = y/20 = z/28

Áp dụng tính chất dãy tỉ số bằng nhau:

=> x/15 = y/20 = z/28 = 2x/30 = 3y/60 = 2x + 3y - z / 30 + 60 - 28 = 186/62 = 3

x/15 = 3 => x = 15 . 3 = 45

y/20 = 3 => y = 20 . 3 = 60

z/28 = 3 => z = 28 . 3 = 84

Vậy x = 45; y = 60; z = 84.

4,5

100*X=450

X=450/100

X=4,5

100*x=450

x=450/100

x=4,5

a) (x-1) -5 = (x+2) (x-2) -x(x-1)

x-1-5 = x^2 - 4 -x^2 +x

0x = -4 +1+5

0x = 6

x thuộc rỗng