Đặt \(\sqrt{x+2016}=y\ge0\)\(\Rightarrow y^2=x+2016\)\(\Rightarrow x=y^2-2016\)
\(\Rightarrow M=y^2-2016+y\)\(=y^2+2.\frac{1}{2}.y+\frac{1}{4}-\frac{8065}{4}=\left(y+\frac{1}{2}\right)^2-\frac{8065}{4}\ge\)\(\left(\frac{1}{2}\right)^2-\frac{8065}{4}=-2016\)\(\forall y\ge0\)
Dấu "=" xảy ra khi \(\sqrt{x+2016}=y=0\Leftrightarrow\)\(x+2016=0\Leftrightarrow x=-2016\)
Vậy ...
\(Cho\)\(M_{\left(x\right)}=x+x^2+x^3+...+x^{2016}\)
a) tìm \(M_{\left(3;-3\right)}\)
b)CM \(M⋮105\Leftrightarrow x=2\)
c)CM \(M⋮196\Leftrightarrow x=3\)
tìm min |x-1|+|x-2|+|x-3|+...+|x-2015|+|x+2016|
Tìm Min P = l x - 2015 l + l 2016 - x l + l x - 2017l
Tìm Min: B=x^2-2x+2016
Tìm giá trị nhỏ nhất của \(A=\left|2016+x\right|+\left|2015-x\right|\)
\(B=\left|2016+x\right|+\left|x-2015\right|\)
\(CMR:A_{min}=B_{min}\)
tìm min B=(x-3)^2+(y+5)^2-2016
Tìm min\(x-\sqrt{x}\)
Tìm x biết:
\(2017.\sqrt{x}+\sqrt{x^2+1}=1-x^{2016}\)
tìm Min F biết F=\(\frac{4\cdot\sqrt{x}+15}{2\cdot\sqrt{x}+9}\)
