\(A=\left|2x-5\right|.\left(4-\left|2x-5\right|\right)\\ A=4.\left|2x-5\right|-\left|2x-5\right|^2\\ A=-\left(\left|2x-5\right|^2-4.\left|2x-5\right|+4\right)+4\\ A=-\left(\left|2x-5\right|-2\right)^2+4\)
Vì \(\left(\left|2x+5\right|-2\right)^2\ge0\) với mọi x nên \(-\left(\left|2x+5\right|-2\right)^2\le0\)
=> \(-\left(\left|2x+5\right|-2\right)^2+4\le4\) hay \(A\le4\)
Dấu ''='' xảy ra khi và chỉ khi \(\left(\left|2x+5\right|-2\right)^2=0\)
=> \(\left|2x-5\right|=2\)
=> \(\left[\begin{array}{nghiempt}2x-5=2\\2x-5=-2\end{array}\right.\) => \(\left[\begin{array}{nghiempt}2x=7\\2x=3\end{array}\right.\) => \(\left[\begin{array}{nghiempt}x=3,5\\x=1,5\end{array}\right.\)
Chúc bạn làm bài tốt
