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\(\Leftrightarrow x^3+2x^2-3x-x^3-3x^2=-4\)
\(\Leftrightarrow x^2+3x-4=0\)
=>(x+4)(x-1)=0
=>x=-4 hoặc x=1
\(\Leftrightarrow x^2-2x+1-9x^2+36x-36=0\\ \Leftrightarrow-8x^2+34x-35=0\\ \Leftrightarrow8x^2-34x+35=0\\ \Leftrightarrow8x^2-20x-14x+35=0\\ \Leftrightarrow\left(2x-5\right)\left(4x-7\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=\dfrac{7}{4}\end{matrix}\right.\)
Bài 2:
Ta có: \(x\left(x-4\right)-x^2+8=0\)
\(\Leftrightarrow x^2-4x-x^2+8=0\)
\(\Leftrightarrow-4x=-8\)
hay x=2
\(x^5+x^4+x+1=0\)
\(\Leftrightarrow x+1=0\)
hay x=-1
a) pt
<=> (x - 5)(x + 5) - (x - 5) = 0
<=> (x - 5)(x + 4) = 0
<=> x - 5 = 0 hoặc x + 4 = 0
<=> x = 5 hoặc x = -4
b) pt
<=> (2x - 1)(2x - 1 - 2x - 1) = 0
<=> (2x - 1).(-2)=0
<=> 2x - 1 = 0
<=> x = 1/2
c) pt
<=> (x - 1)(x + 1)(x^2 + 4) = 0
<=> x - 1 = 0 hoặc x + 1 = 0 hoặc x^2 + 4 = 0
<=> x = 1 hoặc x = -1
\(6x\left(1-3x\right)+9x\left(2x-7\right)+171=0\)
\(\Leftrightarrow6x-18x^2+18x^2-63x+171=0\)
\(\Leftrightarrow-57x=-171\)
\(\Leftrightarrow x=3\)
\(\frac{x+1}{2015}+\frac{x+2}{2014}=\frac{x+3}{2013}+\frac{x+4}{2012}\)
\(\Leftrightarrow\left(\frac{x+1}{2015}+1\right)+\left(\frac{x+2}{2014}+1\right)-\left(\frac{x+3}{2013}+1\right)-\left(\frac{x+4}{2012}+1\right)=0\)
\(\Leftrightarrow\)\(\frac{x+2016}{2015}+\frac{x+2016}{2014}-\frac{x+2016}{2013}+\frac{x+2016}{2012}=0\)
\(\Leftrightarrow\left(x+2016\right)\left(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\right)=0\)
\(\Leftrightarrow x+2016=0\) ( vì \(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\ne0\) )
\(\Leftrightarrow x=-2016\)
x2 (x-y) = 5(y-1) <=> x3 - yx2 - 5y + 5 = 0
<=> y(x2 + 5) = x3 + 5
<=> y = \(\frac{5+x^3}{5+x^2}=\frac{5}{5+x^2}-\frac{5x}{5+x^2}\)+ x
Để y nguyên thì cái đằng sau nguyên còn lại tự làm nha
Ta có :
\(\left(x+1\right)^2=x+1\)
\(\Rightarrow\left(x+1\right)^2-\left(x+1\right)=0\)
\(\Rightarrow\left(x+1\right)x=0\)
\(\Rightarrow\left[\begin{array}{nghiempt}x=-1\\x=0\end{array}\right.\)
Vậy x = - 1 ; x = 0