Ta có :
\(\frac{x-2}{4}=\frac{-16}{2-x}\)
\(\Leftrightarrow\)\(\frac{x-2}{4}=\frac{16}{x-2}\)
\(\Leftrightarrow\)\(\left(x-2\right)\left(x-2\right)=16.4\)
\(\Leftrightarrow\)\(\left(x-2\right)^2=64\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}\left(x-2\right)^2=8^2\\\left(x-2\right)^2=\left(-8\right)^2\end{cases}\Leftrightarrow\orbr{\begin{cases}x-2=8\\x-2=-8\end{cases}}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=8+2\\x=-8+2\end{cases}\Leftrightarrow\orbr{\begin{cases}x=10\\x=-6\end{cases}}}\)
Vậy \(x=-6\) và \(x=10\)
Chúc bạn học tốt ~
Ta có : \(\frac{x-2}{4}=\frac{-16}{2-x}\)
\(\Rightarrow\left(x-2\right).\left(2-x\right)=-16.4\)
\(\Rightarrow\left(x-2\right).2-\left(x-2\right).x=-64\)
\(\Rightarrow2x-4-x^2-2x=-64\)
\(\Rightarrow-4-x^2=-64\)
\(\Rightarrow x^2=-4+64\)
\(\Rightarrow x^2=60\)
\(\Rightarrow\frac{x-2}{4}=\frac{16}{x-2}\)
\(\Rightarrow\left(x-2\right)^2=64\)
\(\Rightarrow\orbr{\begin{cases}x-2=\sqrt{64}\\x-2=-\sqrt{64}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x-2=8\\x-2=-8\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=10\\x=-6\end{cases}}\)
\(=>\left(x-2\right)\left(2-x\right)=4.\left(-16\right)\)
\(=>-x^2+4x-4=-64\)
\(-x^2+4x+60=0\)
\(-x^2-6x+10x+60=0\)
\(-x\left(x+6\right)+10\left(x+6\right)=0\)
\(\left(10-x\right)\left(x+6\right)=0\)
\(
\orbr{\begin{cases}10-x=0=>x=10\\x+6=0=>x=-6\end{cases}}\)
