a) `4x(x-5)-(x-1)(x-3)=23`

`<=> 4x^2-20x-x^2+4x-3=23`

`<=>3x^2-16x-26=0`

`<=> x=(8+-\sqrt142)/3

*Nếu đề là: `4x(x-5)-(x-1)(4x-3)=23`

`<=> 4x^2-20x-4x^2+7x-3=23`

`<=>-13x=26`

`<=>x=-2`

b) `(x-5)(x-4)-(x+1)(x-2)=7`

`<=>x^2-9x+20-x^2+x+2=7`

`<=>-8x=-15`

`<=>x=15/8`

\(\text{a) 4x(x-5)-(x-1)(1x-3)=23}\)

\(\Leftrightarrow4x^2-20x-\left(x^2-3x-x+3\right)=23\)

\(\Leftrightarrow4x^2-20x-x^2+3x+x-3=23\)

\(\Leftrightarrow3x^2-16x-26=0\)

Giải phương trình bậc 2 một ẩn ta được :

\(x_1=\dfrac{8-\sqrt{142}}{3};x_2=\dfrac{8+\sqrt{142}}{3}\)

Bài 1 :

S = \(\frac{6}{2.5}+\frac{6}{5.8}+...+\frac{6}{29.32}\)

   = 2 . \(\left(\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{29.32}\right)\)

   = 2 . \(\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{29}-\frac{1}{32}\right)\)

   = 2 . \(\left(\frac{1}{2}-\frac{1}{32}\right)\)= ....

1)

\(x-17=23\\ \Rightarrow x=23+17\\ \Rightarrow x=40\)

2)

\(2\left(x-1\right)=7+\left(-3\right)\\ \Rightarrow2x-2=4\\ \Rightarrow2x=4+2\\ \Rightarrow2x=8\\ \Rightarrow x=4\)

3)

\(4\left(x+5\right)^3-7=101\\ \Rightarrow4\left(x+5\right)^3=101+7\\ \Rightarrow4\left(x+5\right)^3=108\\ \Rightarrow\left(x+5\right)^3=108\div4\\ \Rightarrow\left(x+5\right)^3=27\\ \Rightarrow\left(x+5\right)^3=3^3\\ \Rightarrow x+5=3\Rightarrow x=3-5\\ \Rightarrow x=-2\)

4)

\(2^{x+1}\times3+15=39\\ \Rightarrow2^{x+1}\times3=39-15\\ \Rightarrow2^{x+1}\times3=24\\ \Rightarrow2^{x+1}=24\div3\\ \Rightarrow2^{x+1}=8\)

\( \Rightarrow2^{2+1}=8\\\Rightarrow2^3=8\Rightarrow x=2 \)

a) x - 17 = 23

x = 23 + 17

x = 40

Vậy x = 40

b) 2 ( x - 1 ) = 7 + ( - 3 )

x - 1 = 4 : 2

x = 2 + 1

x = 3

Vậy x = 3

c) 4 ( x + 3 )^3 - 7 = 101

4 ( x + 3 )^3 = ( 101 + 7 ) : 4

( x + 3 )^3 = 3^3

⇒ x + 3 = 3

⇒ x = 0

Vậy x = 0

d) 2^{ x+ 1 } . 3 + 15 = 39

2^{ x + 1 } = ( 39 - 15 ) : 3

2^{ x + 1 } = 2{ 2 + 1 }

⇒ x + 1 = 2 + 1

⇒ x = 2

Vậy x = 2

\(\text{-7129+1478+7129+(-1479)}\)

\(=\text{-7129+7129+1478+(-1479)}\)

\(=0-1=-1\)

\(\text{|-5|.(-7)+4.(-9)}\)

\(=\text{5.(-7)+4.(-9)}\)

\(=\left(-35\right)+\left(-36\right)=-71\)

\(\text{(-4)²+35:(-7)}\)

\(=\text{16+(-5)=11}\)

x.\(\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}\right)=-1\frac{3}{5}\)

x.\(\left(\frac{5-2}{2.5}+\frac{8-5}{5.8}+\frac{11-8}{8.11}+\frac{14-11}{11.14}+\frac{17-14}{14.17}\right)=\frac{-8}{5}\)

x.\(\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\right)=\frac{-8}{5}\)

x.\(\left(\frac{1}{2}-\frac{1}{17}\right)=\frac{-8}{5}\)

x.\(\left(\frac{17}{34}-\frac{2}{34}\right)=\frac{-8}{5}\)

x.\(\frac{15}{34}=\frac{-8}{5}\)

x\(=\frac{-8}{5}:\frac{15}{34}\)

x\(=\frac{-8}{5}.\frac{34}{15}\)

x\(=\frac{-272}{75}\)

Vậy x\(=\frac{-272}{75}\)