\(\frac{1}{x}+\frac{1}{2.x}+\frac{1}{6x}+\frac{1}{12x}+\frac{1}{30x}\)

= \(\frac{1}{x}\left(1+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{30}\right)\)

= \(\frac{1}{x}\left(1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)

= \(\frac{1}{x}\left(1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)

=\(\frac{1}{x}\left(1+1-\frac{1}{6}\right)\)

=\(\frac{1}{x}.\frac{11}{6}\)

=\(\frac{11}{6x}\)

\(\frac{4}{5}\times\left(20-x\right)=4\)

\(20-x=4:\frac{4}{5}\)

\(20-x=5\)                        Mình Chúc Các Bn Học Giỏi !!!!!!!!!!!!!!!!!!!

\(x=20-5\)

\(x=15\)

(1/2+1/6+1/12+1/20) x (20 - x) =4

4/5 x (20-x)= 4

20-x=4:4/5

20-x=5

x=15

 (\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}\)) x (20-x) = 4

\(\frac{4}{5}\) x (20-x) = 4

                 20-x=4:\(\frac{4}{5}\)

                 20-x=5

                      x=20-5

                      x=15

\(\left|x+\frac{1}{2}\right|+\left|x+\frac{1}{6}\right|+\left|x+\frac{1}{12}\right|+...\left|x+\frac{1}{110}\right|=11x\)

\(\Leftrightarrow\left|x+\frac{1}{2}\right|+\left|x+\frac{1}{6}\right|+\left|x+\frac{1}{12}\right|+...\left|x+\frac{1}{110}\right|\ge0\)

\(\rightarrow11x\ge0\rightarrow x\ge0\)

\(\text{Ta có:}\)

\(x+\frac{1}{2}+...+x+\frac{1}{110}=11x\)

\(\rightarrow10x+\frac{10}{11}=11x\)

\(\rightarrow x=\frac{10}{11}\)

x²-4x+7 = 0 ⇔ x² -4x + 4 + 3 = 0 

⇔ (x-2)²+3=0 ⇔ (x-2)²=-3 (vô lí)

Vậy pt vô nghiệm

*Chứng minh phương trình \(x^2-4x+7=0\) vô nghiệm

Ta có: \(x^2-4x+7=0\)

\(\Leftrightarrow x^2-4x+4+3=0\)

\(\Leftrightarrow\left(x-2\right)^2+3=0\)

mà \(\left(x-2\right)^2+3\ge3>0\forall x\)

nên \(x\in\varnothing\)(đpcm)

Hãy tích cho tui đi

vì câu này dễ mặc dù tui ko biết làm 

Yên tâm khi bạn tích cho tui

Tui sẽ ko tích lại bạn đâu

THANKS

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{x\cdot\left(x+1\right)}=2\)

\(\Leftrightarrow\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...+\frac{1}{x\cdot\left(x+1\right)}=2\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{x}-\frac{1}{x+1}=2\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=2\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-2\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{-3}{2}\)

\(\Leftrightarrow\frac{-3}{-3x-3}=\frac{-3}{2}\)

\(\Leftrightarrow-3x-3=2\)

\(\Leftrightarrow-3x=2+3\)

\(\Leftrightarrow-3x=5\)

\(\Leftrightarrow x=\frac{-5}{3}\)

Vậy \(x=\frac{-5}{3}\)