Áp dụng bất đẳng thức \(\left|a\right|-\left|b\right|\le\left|a-b\right|\) có:
\(A=\left|x-2016\right|-\left|2017-x\right|\le\left|x-2016-2017-x\right|=4033\)

Dấu " = " khi \(\left\{{}\begin{matrix}x-2016\ge0\\x-2017\le0\end{matrix}\right.\Rightarrow2016\le x\le2017\)

Vậy \(MAX_A=4033\) khi \(2016\le x\le2017\)

Change the word in brackets to complete the sentence

-Nam's mother is _unhappy___because he always makes mistakes.(HAPPY)

-I love these people because they are very__friendly___.(FRIEND)

-She is not_different__from her sister.(DIFFER)

-Her new shool is_bigger__than her old school.(BIG)

Ta có: \(x-\sqrt{x}+1=x-2\sqrt{x}.\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{3}{4}\)

\(=\left(\sqrt{x}-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\)

\(\Rightarrow A=\dfrac{1}{\left(\sqrt{x}-\dfrac{1}{2}\right)^2+\dfrac{3}{4}}\le\dfrac{4}{3}\)

Dấu " = " khi \(\left(\sqrt{x}-\dfrac{1}{2}\right)^2=0\Leftrightarrow x=\dfrac{1}{4}\)

Vậy \(MAX_A=\dfrac{4}{3}\) khi \(x=\dfrac{1}{4}\)

a, \(t\left(t+2a^2\right)+a^4=t^2+2a^2t+a^4=\left(a^2+t\right)^2\)

b, \(x^2+3x+2=x^2+2x+x+2=x\left(x+2\right)+\left(x+2\right)\)

\(=\left(x+1\right)\left(x+2\right)\)

c, \(x^4+5x^3+9x^2+7x+2\)

\(=x^4+x^3+4x^3+4x^2+5x^2+5x+2x+2\)

\(=x^3\left(x+1\right)+4x^2\left(x+1\right)+5x\left(x+1\right)+2\left(x+1\right)\)

\(=\left(x^3+4x^2+5x+2\right)\left(x+1\right)\)

\(=\left(x^3+x^2+3x^2+3x+2x+2\right)\left(x+1\right)\)

\(=\left[x^2\left(x+1\right)+3x\left(x+1\right)+2\left(x+1\right)\right]\left(x+1\right)\)

\(=\left(x^2+3x+2\right)\left(x+1\right)^2\)

\(=\left(x+2\right)\left(x+1\right)^3\)

Giải:

Hai người gặp nhau sau:
\(t=\dfrac{s}{v_1+v_2}=2\left(h\right)\)

Chỗ gặp nhau cách A:

\(s_1=v_1.t=50\left(km\right)\)

Vậy...