a/ \(A=\left(x-5\right)^2+\left(2x+1\right)^2-2\left(2x^2+8,5\right)\)
\(=\left(x^2-2.x.5+5^2\right)+\left[\left(2x\right)^2+2.2x.1+1^2\right]-2.2x^2-2.8,5\)
\(=\left(x^2-10x+25\right)+\left(4x^2+4x+1\right)-4x^2-17\)
\(=x^2-10x+25+4x^2+4x+1-4x^2-17\)
\(=x^2-6x+9\)
\(=x^2-2.3x+3^2\)
\(=\left(x-3\right)^2\)
b/ A = 0
\(\Rightarrow\left(x-3\right)^2=0\)
\(\Rightarrow x-3=0\)
\(\Rightarrow x=0+3=3\)
c/ A = 36
\(\Rightarrow\left(x-3\right)^2=36\)
\(\Rightarrow\left(x-2\right)^2=\left(\pm6\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}x-2=6\\x-2=-6\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=6+2=8\\x=-6+2=-4\end{matrix}\right.\)
Vậy................
