The sum of the maximum and minimum values of the function f(x) = |5x – 7| + [x² + 2x] is the interval $\left[\frac{5}{4},2\right]$, where [t] is the greatest integer $\le \mathrm{t}$ is _____________

$$\begin{gathered} f\left(x\right)=\left|5x-7\right|+\left[x^2+2x\right] \\ Here x^2+2x is strictly increa\sin g function in the interrval\left[\frac{5}{4},2\right] \\ at x=\frac{5}{4},\left[x^2+2x\right]=4. \\ and for \left|5x-7\right|minimum value is obtained for x=\frac{7}{5} \\ \therefore For f\left(x\right)minimum value can be obtained at x=\frac{7}{5} and f\left(\frac{7}{5}\right)=4 \\ The maximum value of f\left(x\right) can be obtained at x=2 \\ and at x=2 f\left(x\right)=\left|5x-7\right|+\left[x^2+2x\right]=11 \\ \Rightarrow Maximum+minimum=11+4=15 \end{gathered}$$