Tìm Min à bạn?

\(Q=\left|x-2\right|+\left|x-5\right|+\left|x+1\right|\)

\(=\left|x-2\right|+\left|5-x\right|+\left|x+1\right|\)

\(=\left(\left|x-2\right|+\left|x-5\right|\right)+\left|x+1\right|\)

\(=\left(\left|2-x+5-x\right|\right)+\left|x+1\right|\)

\(=\left|3\right|+\left|x+1\right|=\left|3+x+1\right|=\left|x+4\right|\)

Mà \(\left|x+4\right|\ge0\forall x\Rightarrow MinQ=0\)

Dấu '' = '' xảy ra khi \(x+4=0\Leftrightarrow x=-4\)

\(P=\left|x+1\right|+\left|x+2\right|+\left|x+3\right|\)

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

\(=\left(\left|2x+3\right|+\left|x+3\right|\right)\)

\(=\left|2x+3+x+3\right|\)

\(=\left|3x+6\right|\ge0\)

Dấu '' = '' xảy ra khi \(3x+6=0\Rightarrow3x=-6\Rightarrow x=-2\)

Đặt đại 1 cái tên kk

\(N=\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{100.103}\)

\(\Rightarrow3N=3\left(\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{100.103}\right)\)

\(\Rightarrow3N=\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{100.103}\)

\(\Rightarrow3N=\frac{1}{1}-\frac{1}{4}+...+\frac{1}{100}-\frac{1}{103}\)

\(\Rightarrow3N=\frac{1}{1}-\frac{1}{103}\)

\(\Rightarrow N=\frac{102}{103}:3\)

\(\Rightarrow N=\frac{34}{103}\)

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{1999.2000}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{1999}-\frac{1}{2000}\)

\(=1-\frac{1}{2000}\)

\(=\frac{1999}{2000}\)

B1 :

\(\frac{x}{3}=\frac{y}{6}=\frac{xy}{3\times6}=\frac{162}{18}=9\)

---> x = 3.9 = 27

---> y = 6.9 = 54

B2 :

\(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}=\frac{xyz}{2\times3\times5}=\frac{-240}{30}=-8\)

---> x = -8.2 = -16

---> y = -8.3 = -24

---> z = -8.5 = -40

xin tiick