Question

1)   (8x-5)(x²+2014)=0

2)  \(\frac{2-x}{2015}-1=\frac{1-x}{2016}\)\(-\frac{x}{2017}\)

3)   \(\frac{x-1}{2016}+\frac{x-2}{2015}=\frac{x-3}{2014}\)\(+\frac{x-4}{2013}\)

4)   (2x-5)³-(3x-4)³+(x+1)³=0

Answer 1

Bài 3 : 

\(\frac{x-1}{2016}+\frac{x-2}{2015}=\frac{x-3}{2014}+\frac{x-4}{2013}\)

\(\Leftrightarrow\)\(\left(\frac{x-1}{2016}-1\right)+\left(\frac{x-2}{2015}-1\right)=\left(\frac{x-3}{2014}-1\right)+\left(\frac{x-4}{2013}-1\right)\)

\(\Leftrightarrow\)\(\frac{x-1-2016}{2016}+\frac{x-2-2015}{2015}=\frac{x-3-2014}{2014}+\frac{x-4-2013}{2013}\)

\(\Leftrightarrow\)\(\frac{x-2017}{2016}+\frac{x-2017}{2015}=\frac{x-2017}{2014}+\frac{x-2017}{2013}\)

\(\Leftrightarrow\)\(\frac{x-2017}{2016}+\frac{x-2017}{2015}-\frac{x-2017}{2014}-\frac{x-2017}{2013}=0\)

\(\Leftrightarrow\)\(\left(x-2017\right)\left(\frac{1}{2016}+\frac{1}{2015}-\frac{1}{2014}-\frac{1}{2013}\right)=0\)

Vì \(\frac{1}{2016}+\frac{1}{2015}-\frac{1}{2014}-\frac{1}{2013}\ne0\)

Nên \(x-2017=0\)

\(\Rightarrow\)\(x=2017\)

Vậy \(x=2017\)

Chúc bạn học tốt ~ 

Answer 2

Bài 1 : 

\(\left(8x-5\right)\left(x^2+2014\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}8x-5=0\\x^2+2014=0\end{cases}\Leftrightarrow\orbr{\begin{cases}8x=0+5\\x^2=0-2014\end{cases}}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}8x=5\\x^2=-2014\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{5}{8}\\x=\sqrt{-2014}\left(loai\right)\end{cases}}}\)

Vậy \(x=\frac{5}{8}\)

Chúc bạn học tốt ~ 

Answer 3

Bài 2 : 

\(\frac{2-x}{2015}-1=\frac{1-x}{2016}-\frac{x}{2017}\)

\(\Leftrightarrow\)\(\frac{2-x}{2015}+1=\left(\frac{1-x}{2016}+1\right)-\left(\frac{x}{2017}-1\right)\) ( cộng 2 vế cho 2 ) 

\(\Leftrightarrow\)\(\frac{2-x+2015}{2015}=\frac{1-x+2016}{2016}-\frac{x-2017}{2017}\)

\(\Leftrightarrow\)\(\frac{2017-x}{2015}=\frac{2017-x}{2016}+\frac{2017-x}{2017}\)

\(\Leftrightarrow\)\(\frac{2017-x}{2015}-\frac{2017-x}{2016}-\frac{2017-x}{2017}=0\)

\(\Leftrightarrow\)\(\left(2017-x\right)\left(\frac{1}{2015}-\frac{1}{2016}-\frac{1}{2017}\right)=0\)

Vì \(\frac{1}{2015}-\frac{1}{2016}-\frac{1}{2017}\ne0\)

Nên \(2017-x=0\)

\(\Rightarrow\)\(x=2017\)

Vậy \(x=2017\)

Chúc bạn học tốt ~ 

Answer 4

Bài 2 : 

\(\frac{2-x}{2015}-1=\frac{1-x}{2016}-\frac{x}{2017}\)

Cộng hai vế cho \(2\) : 

+) Vế trái cộng cho \(2\) : 

\(\frac{2-x}{2015}-1+2=\frac{2-x}{2015}+1\)

+) Vế phải cộng cho \(2\) : 

\(\frac{1-x}{2016}-\frac{x}{2017}+2=\left(\frac{1-x}{2016}+1\right)+\left(-\frac{x}{2017}+1\right)=\left(\frac{1-x}{2016}+1\right)-\left(\frac{x}{2017}-1\right)\)

Tới đây quy đồng thì dễ hiểu rồi nhé 

Chúc bạn học tốt ~