Đáp án: $M=2020$
Giải thích các bước giải:
$M=\sqrt{1+{{2019}^{2}}+{{\left( \dfrac{2019}{2020} \right)}^{2}}}+\dfrac{2019}{2020}$
$M=\sqrt{1+2.2019+{{2019}^{2}}-2.2019+{{\left( \dfrac{2019}{2020} \right)}^{2}}}+\dfrac{2019}{2020}$
$M=\sqrt{{{\left( 1+2019 \right)}^{2}}-2.2019+{{\left( \dfrac{2019}{2020} \right)}^{2}}}+\dfrac{2019}{2020}$
$M=\sqrt{{{2020}^{2}}-2.2020.\dfrac{2019}{2020}+{{\left( \dfrac{2019}{2020} \right)}^{2}}}+\dfrac{2019}{2020}$
$M=\sqrt{{{\left( 2020-\dfrac{2019}{2020} \right)}^{2}}}+\dfrac{2019}{2020}$
$M=\left| 2020-\dfrac{2019}{2020} \right|+\dfrac{2019}{2020}$
$M=2020-\dfrac{2019}{2020}+\dfrac{2019}{2020}$
$M=2020$