Question

Tìm GTNN :

A = ( x - 1 )² + 2018

B = ( x + 2 )²⁰¹⁸ + ( y - 3 )²⁰²⁰ + 2019

Answer 1

a, Vì \(\left(x-1\right)^2\ge0\Rightarrow A=\left(x-1\right)^2+2018\ge2018\)

Dấu "=" xảy ra khi x - 1 = 0 <=> x = 1

Vậy GTNN của A=2018 khi x=1

b, Vì \(\hept{\begin{cases}\left(x+2\right)^{2018}\ge0\\\left(y-3\right)^{2020}\ge0\end{cases}\Rightarrow\left(x+2\right)^{2018}+\left(y-3\right)^{2020}\ge0}\)

\(\Rightarrow B=\left(x+2\right)^{2018}+\left(y-3\right)^{2020}+2019\ge2019\)

Dấu "=" xảy ra khi \(\hept{\begin{cases}x+2=0\\y-3=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=-2\\y=3\end{cases}}}\)

Vậy GTNN của B = 2019 khi x=-2,y=3

Answer 2

ta có 

A = ( x - 1 )² + 2018

=( x - 1 )² + 2018≥2018

dấu "=" xảy ra khi ( x - 1 )²=0=>x=1

vs min A=2018 khi x=1