\(\frac{x-1}{2}\) = \(\frac{8}{x-1}\)

(\(x-1\)).(\(x-1\)) = 8.2

(\(x\) - 1)\(^2\) = 16

(\(x-1\))\(^2\) = 4\(^2\)

\(\left[\begin{array}{l}x-1=-4\\ x-1=4\end{array}\right.\)

\(\left[\begin{array}{l}x=-4+1\\ x=4+1\end{array}\right.\)

\(\left[\begin{array}{l}x=-3\\ x=5\end{array}\right.\)

Vậy \(x\in\) {-3; 5}

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

=>\(\left(x-1\right)\left(x-1\right)=2\cdot8=16\)

=>\(\left[{}\begin{matrix}x-1=4\\x-1=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-3\end{matrix}\right.\)

x=33/11:6

x=1/2

❤❤❤

\(\frac{6}{x}\) = - \(\frac{33}{11}\)

\(\frac{6}{x}\) = - 3

\(x\) = 6 : -3

\(x=-2\)

Vậy \(x=-2\)

xy+3x-7y=21

x.(y+3)-7y-21=21-21

x.(y+3)-7.(y+3)=0

(x-7).(y+3)=0

=>x-7, y+3 ∈ 0

=>x=-7 , y= -3

Vậy ( x, y) ∈ ( -7, -3)

\(2^{3n}=\left(2^3\right)^n=8^n\)

\(3^{2n}=\left(3^2\right)^n=9^n\)

mà \(8^n< 9^n\left(8< 9\right)\)

nên \(2^{3n}< 3^{2n}\)

\(-\frac{11}{12}<\frac{x}{5}<-\frac{11}{15}\)

\(-11.5<\frac{12x}{5.12}<-\frac{11.4}{15.4}\)

\(-\frac{55}{60}<\frac{12x}{60}<-\frac{44}{60}\)

\(-55<12x<-44\)

\(-\frac{55}{12}

\(\rArr x=-4\left(x\in Z\right)\)

Do n chia 3;5;7 lần lượt dư 2;4;6

\(\Rightarrow n+1\) chia hết cho cả 3;5 và 7

\(\Rightarrow n+1=ƯC\left(3;5;7\right)=Ư\left(105\right)\) 

Mà n nhỏ nhất \(\Rightarrow n+1\) nhỏ nhất

\(\Rightarrow n+1=105\)

\(\Rightarrow n=104\)

Gọi mẫu là x

Theo đề, ta có: \(\dfrac{-11}{12}< \dfrac{5}{x}< \dfrac{-11}{15}\)

=>\(\dfrac{-55}{60}< \dfrac{-55}{-11x}< \dfrac{-55}{75}\)

=>\(\dfrac{55}{60}>\dfrac{55}{-11x}>\dfrac{55}{75}\)

=>60<-11x<75

=>\(-\dfrac{60}{11}>x>-\dfrac{75}{11}\)

=>\(x=-6\)

Vậy: Phân số cần tìm là \(\dfrac{5}{-6}\)

\(2x^2-3x+1=0\\ \Delta=b^2-4ac=\left(-3\right)^2-4\cdot2\cdot1=1>0\\ x_1=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{-\left(-3\right)-1}{2\cdot2}=0,5\\ x_2=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-\left(-3\right)+1}{2\cdot2}=1\\ \text{vậy phương trình có 2 nghiệm là }x_1=0,5;x_2=1\)

\(2x^2-3x+1=0\)

Ta có: \(\Delta=\left(-3\right)^2-4\cdot2\cdot1=1\left(>0\right)\)

Do \(\Delta>0\) nên phương trình có hai nghiệm phân biệt:

x1 = \(\frac{-b+\sqrt{\Delta}}{2a}=\frac{-\left(-3\right)+\sqrt1}{4}=\frac{3+1}{4}=1\)

x2 = \(\frac{-b-\sqrt{\Delta}}{2a}=\frac{-\left(-3\right)-\sqrt1}{4}=\frac{3-1}{4}=\frac24=\frac12\)

Đề lỗi rồi em

2x -3= 5x +6

sử dụng quy tắc chuyển vế

2x-(-5x)= 3+6

2x+5x=9

x(2+5)=9

x .7=9

x= 9:7

=> x= 9/7

<=> 2x - 5x = 6+3

<=> -3x = 9

<=> x = -1