x = 4

\(\Leftrightarrow\left(2x-7\right)^{2017}\left[\left(2x-7\right)^2-1\right]=0\)

=>(2x-7)(2x-6)(2x-8)=0

hay \(x\in\left\{3;\dfrac{7}{2};4\right\}\)

Bài 5.5:

\(\left(2x-3\right)\left(x+1\right)+\left(4x^3-6x^2-6x\right):\left(-2x\right)=18\)

\(\Leftrightarrow\left(2x^2+2x-3x-3\right)+2x\cdot\left(2x^2-3x-3\right):\left(-2x\right)=18\)

\(\Leftrightarrow2x^2-x-3-2x^2+3x+3=18\)

\(\Leftrightarrow2x=18\)

\(\Leftrightarrow x=\dfrac{18}{2}\)

\(\Leftrightarrow x=9\) 

TH1: 2x² +2017=2019

2x² =2019-2017

2x² =2

x² =2 : 2

x² =1

=>x=1

TH2: 2x² +2017= -2019

tự tính tiếp nha

\(\left|2x^2+2017\right|=2019\)

\(\Rightarrow\orbr{\begin{cases}2x^2+2017=2019\\2x^2+2017=-2019\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}2x^2=2\\2x^2=-4036\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x^2=1\\x^2=-2018\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\pm1\\x\in\varnothing\end{cases}}\)

vậy_

Đặt 2017-x=a; 2019-x=b

\(\Leftrightarrow a+b=4036-2x\)

\(\Leftrightarrow-\left(a+b\right)=2x-4036\)

Phương trình trở thành: \(a^3+b^3-\left(a+b\right)^3=0\)

\(\Leftrightarrow\left(a+b\right)^3-3ab\left(a+b\right)-\left(a+b\right)^3=0\)

\(\Leftrightarrow-3ab\left(a+b\right)=0\)

mà -3<0

nên \(ab\left(a+b\right)=0\)

\(\Leftrightarrow\left(2017-x\right)\left(2019-x\right)\left(4036-2x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2017-x=0\\2019-x=0\\4036-2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2017\\x=2019\\x=2018\end{matrix}\right.\)

Vậy: S={2017;2018;2019}

Cho \(\left(2017-x\right)^3=x;\left(2019-x\right)^3=y;\left(2x-4036\right)^3=z\)

Ta có: \(x+y+z=0\)

\(=>x+y=-z\) \(=>\left(x+y\right)^3=-z^3\)

Ta có: \(x^3+y^3+z^3=\left(x+y\right)^3-3xy\left(x+y\right)+z^3=-z^3-3xy\left(-z\right)+z^3=3xyz\)

Vì (2017-x)³ + (2019-x)³ + (2x-4036)³ =0 

=>\(3\left(2017-x\right)\left(2019-x\right)\left(2x-4036\right)=0\)

Gải phương trình được x=2017; x=2019; x=2018

\(a,\dfrac{3}{2}x+\dfrac{1}{4}=\dfrac{-1}{7}\\ \dfrac{3}{2}x=\dfrac{-1}{7}-\dfrac{1}{4}\\ \dfrac{3}{2}x=-\dfrac{11}{28}\\ x=\dfrac{-11}{28}:\dfrac{3}{2}\\ x=-\dfrac{11}{42}\\ b,x:\dfrac{4}{7}-\dfrac{1}{7}=0,5\\ x:\dfrac{4}{7}-\dfrac{1}{7}=\dfrac{1}{2}\\ x:\dfrac{4}{7}=\dfrac{1}{2}+\dfrac{1}{7}\\ x:\dfrac{4}{7}=\dfrac{9}{14}\\ x=\dfrac{9}{14}\times\dfrac{4}{7}\\ x=\dfrac{18}{49}\)

VD: 3/2 có nghĩa là 3 phần 2 nha làm vậy cho mn dễ hiểu. Mọi người theo dõi mik, để có bất ngờ nha. Chúc mọi người 1 ngày vui vẻ, ngày càng học giỏi nhé!