ta có : \(C=\left|x-1\right|+\left|2-x\right|+\left|x-3\right|+\left|4-x\right|+...+\left|x-99\right|+\left|100-x\right|\)
\(\ge\left|x-1+2-x+x-3+4-x+...+x-99+100-x\right|=\left|50\right|=50\)
\(\Rightarrow C_{min}=50\)
dấu bằng xảy ra khi : \(x-1;x-2;x-3;...;x-100>0\Leftrightarrow x>100\)
vậy GTNN của \(C\) là \(50\) khi \(x>100\)
\(A=\left|4x-\frac{7}{3}\right|+2004\)
\(B=\left|x-1\right|+\left|x-2\right|+\left|x-3\right|+\left|x-4\right|\)
\(C=\left|x\right|+\left|x-1\right|+\left|x-2\right|+....+\left|x+99\right|\)
Tìm x : \(\left(x-3\right)^2-\left(2x+1\right)^2-2\left(x-1\right)\left(x+2\right)=3\left(x-3\right)-\left(4x-1\right)\left(x+2\right)\)
Tìm x biết
a) \(-x^2.\left(x^2-4\right)=-25.\left(x^2-4\right)\)
b) \(x^2.\left(2\left|x\right|-3\right)=\left|x^2\right|.\left(2\left|x\right|-3\right)\)
c) \(\left(2x-6\right)^2=\left(3x+1\right)^{15}\)
d) \(2\left|x-3\right|-\left|4-x\right|=1\)
Tìm x, biết
|x2-25|+|x2-100|=75
b,\(\left|\frac{x}{2}-2\right|\in Z;\left|\frac{x}{2}-2\right|< 2\)
c, \(\left|x-\frac{1}{3}\right|+\frac{4}{5}=\left|\left(-3,2\right)+\frac{2}{5}\right|\)
Tìm x:
\(\left(x-1\right)^3-2\left(x-1\right)\left(x+2\right)=\left(x+2\right)^3-3\left(x-1\right)^2+2\left(x+2\right)^2\)
Tìm x : \(\left(x-3\right)^2-\left(2x+1\right)^2-2\left(x-1\right)\left(x+2\right)=3\left(x-3\right)-\left(4x-1\right)\left(x+2\right)\)
a,\(\left|x+\frac{1}{2}\right|+\left|x+\frac{1}{3}\right|+\left|x+\frac{1}{6}\right|=4x\)
b,\(\frac{7}{\left(x+3\right)\left(x+10\right)}+\frac{11}{\left(x+10\right)\left(x+21\right)}+\frac{13}{\left(x+21\right)\left(x+34\right)}=\frac{x}{\left(x+3\right)\left(x+34\right)}\)
Tìm \(x\in Q\) sao cho:
\(\left|x+\frac{1}{101}\right|+\left|x+\frac{2}{101}\right|+\left|x+\frac{3}{101}\right|+...+\left|x+\frac{100}{101}\right|=101x\)
Tìm x : \(\frac{\left(x-3\right)^2}{2}-1\frac{1}{3}\left(x+2\right)^2-\frac{5}{4}\left(x-1\right)\left(x+1\right)=1\frac{1}{2}x\left(x-2\right)-x-4\)
