Question

1. Tìm giá trị lớn nhất

a. A = - I x+3 I + 2017

b. B = 120 - I 30 - x I - I 40 + y I

c. C = 2016 - I 2x + 1 I

d. D = - I x + 1 I - I y + 2 I =11

Answer 1

a, Ta có: \(-\left|x+3\right|\le0\)

\(\Rightarrow A=-\left|x+3\right|+2017\le2017\)

Dấu " = " xảy ra khi \(-\left|x+3\right|=0\Rightarrow x=-3\)

Vậy \(MAX_A=2017\) khi x = -3

b, Ta có: \(\left\{{}\begin{matrix}-\left|30-x\right|\le0\\-\left|40+y\right|\le0\end{matrix}\right.\Rightarrow-\left|30-x\right|-\left|40+y\right|\le0\)

\(\Rightarrow B=120-\left|30-x\right|-\left|40+y\right|\le120\)

Dấu " = " xảy ra khi \(\left\{{}\begin{matrix}\left|30-x\right|=0\\\left|40+y\right|=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=30\\y=-40\end{matrix}\right.\)

Vậy \(MAX_B=120\) khi x = 30, y = -40

c, Ta có: \(-\left|2x+1\right|\le0\)

\(\Rightarrow C=2016-\left|2x+1\right|\le2016\)

Dấu " = " xảy ra khi \(\left|2x+1\right|=0\Rightarrow x=\dfrac{-1}{2}\)

Vậy \(MAX_C=2016\) khi \(x=\dfrac{-1}{2}\)

d, Sai đề