8x + 2 =18
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\(\Leftrightarrow x^3-2x^2-6x^2+12x+9x-18=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^2-6x+9\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-3\right)^2=0\)
=>x=2 hoặc x=3
\(A=\dfrac{4\left(x^2+2x+3-3\right)+18}{x^2+2x+3}=\dfrac{4\left(x^2+2x+3\right)+6}{x^2+2x+3}=4+\dfrac{6}{\left(x+1\right)^2+2}\)
Ta có \(\left(x+1\right)^2+2\ge2\Rightarrow\dfrac{6}{\left(x+1\right)^2+2}\le3\Leftrightarrow4+\dfrac{6}{\left(x+1\right)^2+2}\le7\)
Dấu ''='' xảy ra khi x = -1
\(...P=x^2-8x+16+x^2+2xy+y^2+2y^2-2y+2\)
\(P=\left(x-4\right)^2+\left(x+y\right)^2+2\left(y^2-y+1\right)\left(1\right)\)
Xét \(y^2-y+1=y^2-y+\dfrac{1}{4}-\dfrac{1}{4}+1=\left(y-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\left(\left(y-\dfrac{1}{2}\right)^2\ge0\right)\)
\(\Rightarrow2\left(y^2-y+1\right)\ge2.\dfrac{3}{4}=\dfrac{3}{2}\)
mà \(\left(x-4\right)^2\ge0;\left(x+y\right)^2\ge0\)
\(\left(1\right)\Rightarrow P\ge\dfrac{3}{2}\Rightarrow Min\left(P\right)=\dfrac{3}{2}\)
8x + 2 = 18
8x = 18 - 2
8x = 16
x = 16 : 8
x = 2
8x+2=18
8x=18-2
8x=16
x=16:8
x=2