\(9x^2-6x-3=0\)
\(\Leftrightarrow\left[\left(3x\right)^2-2\cdot3x\cdot1+1^2\right]-4=0\)
\(\Leftrightarrow\left(3x-1\right)^2-2^2=0\)
\(\Leftrightarrow\left(3x-1-2\right)\left(3x-1+2\right)=0\)
\(\Leftrightarrow\left(3x-3\right)\left(3x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-3=0\\3x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{1}{3}\end{matrix}\right.\)
\(---\)
\(x^3+9x^2+27x+19=0\)
\(\Leftrightarrow x^3+3\cdot x^2\cdot3+3\cdot x\cdot3^2+3^3-8=0\)
\(\Leftrightarrow\left(x+3\right)^3=8\)
\(\Leftrightarrow x+3=2\)
\(\Leftrightarrow x=-1\)
\(---\)
\(x\left(x+5\right)\left(x-5\right)-\left(x+2\right)\left(x^2-2x+4\right)=3\)
\(\Leftrightarrow x\left(x^2-5^2\right)-\left(x^3+2^3\right)=3\)
\(\Leftrightarrow x^3-25x-x^3-8=3\)
\(\Leftrightarrow-25x-8=3\)
\(\Leftrightarrow-25x=11\)
\(\Leftrightarrow x=-\dfrac{11}{25}\)
\(---\)
\(x^2+2x+y^2-6y+4z^2-4z+11=0\)
\(\Leftrightarrow\left(x^2+2x+1\right)+\left(y^2-6y+9\right)+\left(4z^2-4z+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)^2+\left(y-3\right)^2+\left(2z-1\right)^2=0\)
Ta thấy: \(\left(x+1\right)^2\ge0\forall x\)
\(\left(y-3\right)^2\ge0\forall y\)
\(\left(2z-1\right)^2\ge0\forall z\)
\(\Rightarrow\left(x+1\right)^2+\left(y-3\right)^2+\left(2z-1\right)^2\ge0\forall x;y;z\)
Mặt khác: \(\left(x+1\right)^2+\left(y-3\right)^2+\left(2z-1\right)^2=0\)
nên \(\left\{{}\begin{matrix}x+1=0\\y-3=0\\2z-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-1\\y=3\\z=\dfrac{1}{2}\end{matrix}\right.\)
#\(Toru\)
