46/15 nhé bạn

TL
37/15

HT

46/15

\(\frac{1}{2}\times\frac{1}{3}+\frac{1}{3}\times\frac{1}{4}+...+\frac{1}{8}\times\frac{1}{9}=\frac{1}{2\times3}+\frac{1}{3\times4}+....+\frac{1}{8\times9}\)

\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-....-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}=\frac{1}{2}-\frac{1}{9}=\frac{7}{18}\)

a) \(\dfrac{11}{3}-\dfrac{2}{3}\times\dfrac{5}{6}\)

\(=\dfrac{11}{3}-\dfrac{10}{18}\)

\(=\dfrac{11}{3}-\dfrac{5}{9}\)

\(=\dfrac{33}{9}-\dfrac{5}{9}\)

\(=\dfrac{28}{9}\)

b) \(\dfrac{13}{2}+\dfrac{7}{6}:\dfrac{2}{3}\)

\(=\dfrac{13}{2}+\dfrac{7}{6}\cdot\dfrac{3}{2}\)

\(=\dfrac{13}{2}+\dfrac{7}{4}\)

\(=\dfrac{26}{4}+\dfrac{7}{4}\)

\(=\dfrac{33}{4}\)

c) \(\dfrac{28}{9}-\dfrac{3}{4}+\dfrac{1}{3}\)

\(=\dfrac{28}{9}+\dfrac{3}{9}-\dfrac{3}{4}\)

\(=\dfrac{31}{9}-\dfrac{3}{4}\)

\(=\dfrac{124}{36}-\dfrac{27}{36}\)

\(=\dfrac{97}{36}\)

d) \(\dfrac{5}{8}:\dfrac{2}{3}\times\dfrac{1}{5}\)

\(=\dfrac{5}{8}\times\dfrac{3}{2}\times\dfrac{1}{5}\)

\(=\dfrac{15}{80}\)

\(=\dfrac{3}{16}\)

a) \(\dfrac{11}{3}-\dfrac{2}{3}\times\dfrac{5}{6}=\dfrac{11}{3}-\dfrac{5}{9}=\dfrac{28}{9}\)

b) \(\dfrac{13}{2}+\dfrac{7}{6}:\dfrac{2}{3}=\dfrac{13}{2}+\dfrac{7}{6}\times\dfrac{3}{2}=\dfrac{13}{2}+\dfrac{7}{4}=\dfrac{33}{4}\)

c) \(\dfrac{28}{9}-\dfrac{3}{4}+\dfrac{1}{3}=\dfrac{97}{36}\)

d) \(\dfrac{5}{8}:\dfrac{2}{3}\times\dfrac{1}{5}=\dfrac{5}{8}\times\dfrac{3}{2}\times\dfrac{1}{5}=\dfrac{3}{16}\)

a) \(\dfrac{11}{3}-\dfrac{2}{3}\times\dfrac{5}{6}\)

\(=\dfrac{11}{3}-\dfrac{5}{9}\)

\(=\dfrac{33}{9}-\dfrac{5}{9}\)

\(=\dfrac{28}{9}\)

b) \(\dfrac{13}{2}+\dfrac{7}{6}:\dfrac{2}{3}\)

\(=\dfrac{13}{2}+\dfrac{7}{6}\times\dfrac{3}{2}\)

\(=\dfrac{13}{2}+\dfrac{7}{4}\)

\(=\dfrac{26}{4}+\dfrac{7}{4}\)

\(=\dfrac{33}{4}\)

c) \(\dfrac{28}{9}-\dfrac{3}{4}+\dfrac{1}{3}\)

\(=\dfrac{28}{9}+\dfrac{3}{9}-\dfrac{3}{4}\)

\(=\dfrac{31}{9}-\dfrac{3}{4}\)

\(=\dfrac{124}{36}-\dfrac{27}{36}\)

\(=\dfrac{97}{36}\)

d) \(\dfrac{5}{8}:\dfrac{2}{3}\times\dfrac{1}{5}\)

\(=\dfrac{5}{8}\times\dfrac{3}{2}\times\dfrac{1}{5}\)

\(=\dfrac{3}{16}\)

\(a)\frac{1}{5}\times\frac{1}{2}:\frac{1}{3}=\frac{1}{5}\times\frac{1}{2}\times\frac{3}{1}=\frac{1\times1\times3}{5\times2\times1}=\frac{1\times3}{5\times2}=\frac{3}{10}\)

\(b)\frac{2}{9}:\frac{2}{3}\times\frac{1}{2}=\frac{2}{9}\times\frac{3}{2}\times\frac{1}{2}=\frac{2\times3\times1}{9\times2\times2}=\frac{1\times1\times1}{3\times1\times2}=\frac{1}{6}\)

\(c)\frac{1}{2}\times\frac{1}{3}+\frac{1}{4}=\frac{1}{6}+\frac{1}{4}=\frac{2}{12}+\frac{3}{12}=\frac{2+3}{12}=\frac{5}{12}\)

d, Tương tự như câu c

P/S : Bất phương trình????

\(\frac{1}{5}\times\frac{1}{2}:\frac{1}{3}\)

\(=\frac{1}{10}\times\frac{3}{1}\)

\(=\frac{3}{10}\)

\(\frac{2}{9}:\frac{2}{3}\times\frac{1}{2}\)

\(=\frac{2}{9}\times\frac{3}{2}\times\frac{1}{2}\)

\(=\frac{1}{3}\times\frac{1}{1}\times\frac{1}{2}\)

\(=\frac{1}{3}\times\frac{1}{2}\)

\(=\frac{1}{6}\)

  1/2x1/3+1/3x1/4+1/4x1/5+1/5x1/6+1/6x1/7+1/7x1/8+1/8x1/9

=7/18

3/7x7/3=1

3/7:7/3=1

2/3x1/6x9/11=2/3/54/11=36/11

2x3x4 trên 2x3x4x5=1/5

mk chắc chắn, cho mk nha, kb nhé

\(\frac{3}{7}x\frac{7}{3}=1\)

\(\frac{3}{7}:\frac{7}{3}=1\)

\(\frac{2}{3}x\frac{1}{6}x\frac{9}{11}=\frac{2x1x9}{3x6x11}=\frac{18}{198}=\frac{1}{11}\)

\(\frac{2x3x4}{2x3x4x5}=\frac{1}{5}\)

a) (*) m = 0 => x = \(\dfrac{7}{8}\) (loại)

(*) \(m\ne0\) Phương trình có nghiệm

\(\Delta=\left[2\left(m-4\right)\right]^2-4m\left(m+7\right)=-60m+64\ge0\Leftrightarrow m\le\dfrac{16}{15}\) 

Hệ thức Viet kết hợp 4x₁ + 3x₂ = 1

\(\Leftrightarrow\left\{{}\begin{matrix}x_1x_2=\dfrac{m+7}{m}\\x_1+x_2=\dfrac{8-2m}{m}\\x_1=2x_2\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x_1x_2=\dfrac{m+7}{m}\\x_1=\dfrac{16-4m}{3m}\\x_2=\dfrac{8-2m}{3m}\end{matrix}\right.\)

\(\Leftrightarrow\dfrac{16-4m}{3m}.\dfrac{8-2m}{3m}=\dfrac{m+7}{m}\)

\(\Leftrightarrow2\left(8-2m\right)^2=9m\left(m+7\right)\)

\(\Leftrightarrow8m^2-64m+128=9m^2+63m\)

\(\Leftrightarrow m^2+127m-128=0\Leftrightarrow\left[{}\begin{matrix}m=1\\m=128\left(\text{loại}\right)\end{matrix}\right.\)<=> m = 1