Câu 1:
a. Ta có:\(\left|x-2017\right|\ge0\)
\(\Rightarrow2016+\left|x-2017\right|\ge2016\)
\(\Rightarrow A\ge2016\)
Dấu " = " xảy ra <=> x - 2017 = 0 <=> x = 2017
Vậy MinA = 2016 khi x = 2017
b. Ta có: \(\left(x-10\right)^2\ge0\)
\(\Rightarrow2017+\left(x-10\right)^2\ge2017\)
\(\Rightarrow B\ge2017\)
Dấu " = " xảy ra <=> (x - 10)2 = 0 <=> x = 10
Vậy MinB = 2017 khi x = 10
c.Ta có: \(\left(x-1\right)^4\ge0\)
\(\Rightarrow-50+\left(x-1\right)^4\ge-50\)
\(\Rightarrow C\ge-50\)
Dấu " = " xảy ra <=> (x - 1)4 = 0 <=> x = 1
Vậy MinC = -50 khi x = 1
Câu 2:
a. Ta có: \(-\left(x-10\right)^2\le0\)
\(\Rightarrow-100-\left(x-10\right)^2\le-100\)
\(\Rightarrow M\ge-100\)
Dấu " = " xảy ra <=> ( x - 10)2 = 0 <=> x = 10
Vậy MaxM = -100 khi x = 10
b. Ta có: \(-\left(x-5\right)^2\le0\)
\(\Rightarrow2017-\left(x-5\right)^2\ge2017\)
\(\Rightarrow N\ge2017\)
Dấu " = " xảy ra <=> (x - 5)2 = 0 <=> x = 5
Vậy MaxN = 2017 khi x = 5
c. Ta có: \(-\left(x+7\right)^4\le0\)
\(\Rightarrow-25-\left(x+7\right)^4\le-25\)
\(\Rightarrow Q\le-25\)
Dấu " = " xảy ra <=> (x + 7)4 = 0 <=> x = -7
Vậy MaxQ = -25 khi x = -7