Ta có:
\(\sqrt{\left(x-1890\right)^2}+\sqrt{\left(x-1969\right)^2}=\left|x-1890\right|+\left|x-1969\right|\)
\(=\left|x-1890\right|+\left|1969-x\right|\)
Áp dụng BĐT \(\left|A\right|+\left|B\right|\ge\left|A+B\right|\) ta được
\(\left|x-1890\right|+\left|1969-x\right|\ge\left|x-1890+1969-x\right|\)
<=>\(\left|x-1890\right|+\left|1969-x\right|\ge79\)
=> P\(\ge79\)
Dấu "=" xảy ra khi
\(\left[{}\begin{matrix}x-1890=0\\1969-x=0\end{matrix}\right.\)
<=> x=1890 hay x=1969