a ) \(\left(x+3\right)^2=\left(x-2\right)\left(x+4\right)\)
\(\Leftrightarrow x^2+6x+9=x^2+2x-8\)
\(\Leftrightarrow4x=-17\)
\(\Leftrightarrow x=-\frac{17}{4}\)
b ) \(\left(x+4\right)^2=2x^2+16\)
\(\Leftrightarrow x^2+8x+16=2x^2+16\)
\(\Leftrightarrow8x=x^2\)
\(\Leftrightarrow8x-x^2=0\)
\(\Leftrightarrow x\left(8-x\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x=8\end{array}\right.\)
Vậy x = 0 và x = 8
\(a,\left(x+3\right)^2=\left(x-2\right)\left(x+4\right)\)
\(\Rightarrow\left(x+3\right)^2=x^2+2x-8\) \(\Rightarrow\left(x+3\right)^2=x^2+2x+1-9\)
\(\Rightarrow\left(x+3\right)^2=\left(x+1\right)^2-9\) \(\Rightarrow\left(x+1\right)^2-\left(x+3\right)^2=9\)
\(\Rightarrow\left(x+1+x+3\right)\left(x+1-x-3\right)=9\)
\(\Rightarrow\left(2x+4\right)\left(-2\right)=9\) \(\Rightarrow2x+4=-\frac{9}{2}\)
\(\Rightarrow2x=-\frac{17}{2}\) \(\Rightarrow x=-\frac{17}{4}\)
\(b,\left(x+4\right)^2=2x^2+16\)
\(\Rightarrow\left(x+4\right)^2=x^2+x^2+4^2\)
\(\Rightarrow\left(x+4\right)^2=x^2+\left(x+4\right)^2-8x\)
\(\Rightarrow\left(x+4\right)^2=x\left(x-8\right)+\left(x+4\right)^2\)
\(\Rightarrow x\left(x-8\right)=0\) \(\Rightarrow\) \(\left[\begin{array}{nghiempt}x=0\\x-8=0\end{array}\right.\) \(\Rightarrow\) \(\left[\begin{array}{nghiempt}x=0\\x=8\end{array}\right.\)