(x - 2)2 - 3(x + 1)2 = 2 - (x - 2)(x - 1)
<=> (x - 2)2 + (x - 2)(x - 1) = 2 + 3(x + 1)2
<=> (x - 2)(x - 2 + x - 1) = 2 + 3(x2 + 1 + 2x)
<=> (x - 2).(2x - 3) = 2 + 3x2 + 3 + 6x
<=> 2x2 - 4x - 3x + 6 = 2 + 3x2 + 3 + 6x
<=> x2 + 13x - 1 = 0
<=> \(\left(x+\dfrac{13}{2}\right)^2=\dfrac{173}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-13+\sqrt{173}}{2}\\x=\dfrac{-13-\sqrt{173}}{2}\end{matrix}\right.\)
Vậy ...
<=> x2 - 4x+4-3(x2+2x+1)=2-(x2-x-2x+2)
<=> x2-4x+4x-4-3x2-6x-3=2-(x2-3x+2)
<=> -2x2-10x+1=2-x2+3x-2
<=> -x2 -13x+1=0
<=> x2 +13x-1
Tự tính đen ta nha
\(\left(x-2\right)^2-3\left(x+1\right)^2=2-\left(x-2\right)\left(x-1\right)\)
\(\Rightarrow x^2-2x-2x+4-3-3.x^2+x+x+1=2-x^2-2x-x+3\)
\(\Rightarrow\left(x^2-3x^2\right)-\left(2x+2x-x-x\right)+\left(4-3+1\right)=5-x^2-\left(2x+x\right)\)
\(\Rightarrow-2x^2-2x+2=5-x^2-3x\)
\(\Rightarrow-2x^2+x^2-2x+3x=-2+5\)
\(\Rightarrow\left(-2x^2+x^2\right)-\left(2x-3x\right)=3\)
\(\Rightarrow-x^2+x=3\)
\(\Rightarrow-\left(x^2-x\right)=3\)
\(\Rightarrow-\left(x^2-\dfrac{1}{2}x-\dfrac{1}{2}x\right)=3\)
\(\Rightarrow-\left(x^2-\dfrac{1}{2}x-\dfrac{1}{2}x+\dfrac{1}{4}-\dfrac{1}{4}\right)=3\)
\(\Rightarrow-\left[x\left(x-\dfrac{1}{2}\right)-\dfrac{1}{2}\left(x-\dfrac{1}{2}\right)-\dfrac{1}{4}\right]=3\)
\(\Rightarrow\left(x-\dfrac{1}{2}\right)^2-\dfrac{1}{4}=3\)
\(\Rightarrow\left(x-\dfrac{1}{2}\right)^2=\dfrac{13}{4}\)
\(\Rightarrow\left[{}\begin{matrix}x-\dfrac{1}{2}=\sqrt{\dfrac{13}{4}}\\x-\dfrac{1}{2}=-\sqrt{\dfrac{13}{4}}\end{matrix}\right.\)
Tự làm tiếp nhé!
P/s: Cách hơi dài, nhưng ai có cách khác thì làm nhé!
