Tìm Max của biểu thức \(A=\frac{3-4x}{x^2+1}\)

\(\left(\frac{2}{5}-\frac{1}{2}\right)^2+\left(\frac{1}{2}+\frac{3}{5}\right)^2\)

\(\Leftrightarrow\left(\frac{2}{5}\right)^2+\left(\left(\frac{-1}{2}\right)^2+\left(\frac{1}{2}\right)^2\right)+\left(\frac{3}{5}\right)^2\)

\(\Leftrightarrow\left(\frac{2}{5}\right)^2+\left(\frac{3}{5}\right)^2\)

\(\Leftrightarrow\left(\frac{2}{5}+\frac{3}{5}\right)^2\)

\(=1\)

\(x^2-4x+3=0\)

\(\Leftrightarrow x\left(x-1\right)-3\left(x+1\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(x-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)

Vậy....

\(\frac{2^{50}.3^{61}+2^{90}.3^{16}}{2^{51}.3^{61}+2^{91}.3^{16}}\)

\(\Leftrightarrow\frac{2^{50}+2^{90}}{2^{50}.2+2^{90}.2}\)

\(\Leftrightarrow\frac{1+1}{2+2}\)

\(\Leftrightarrow\frac{1}{2}\)

_{P/s: Không chắc nhé! '-'}