a; \(\dfrac{1919}{2121}\) = \(\dfrac{1919:101}{2121:101}\) = \(\dfrac{19}{21}\)

b; 17 x 5 - \(\dfrac{17}{120}\) - 103

= 85 - \(\dfrac{17}{120}\) - 103

= \(\dfrac{10200}{120}\) - \(\dfrac{17}{120}\) - \(\dfrac{12360}{120}\)

= \(\dfrac{10183}{120}\) - \(\dfrac{12360}{120}\)

= \(\dfrac{-2177}{120}\)

c; 2929 - \(\dfrac{101}{2\times1919}\) + 404

= 2929 - \(\dfrac{1}{38}\) + 404

= \(\dfrac{111302}{38}\) - \(\dfrac{1}{38}\) + \(\dfrac{15352}{38}\)

= \(\dfrac{111301}{38}\) + \(\dfrac{15352}{38}\)

 = \(\dfrac{126653}{38}\)

18 x \(\left(\frac{1919}{2121}+\frac{888}{999}\right)\)

= 18 x \(\frac{113}{63}\)

= \(\frac{226}{7}\)

Đây có phải tính nhanh không bạn?

\(18\cdot\left(\frac{1919}{2121}+\frac{888}{999}\right)\)

Rút gọn:

\(\frac{1919}{2121}=\frac{1919:101}{2121:101}=\frac{19}{21}\)

\(\frac{888}{999}=\frac{888:111}{999:111}=\frac{8}{9}\)

Ta có:

\(18\cdot\left(\frac{19}{21}+\frac{8}{9}\right)\)

=\(18\cdot\left(\frac{57}{63}+\frac{56}{63}\right)\)

\(=18\cdot\frac{113}{63}\)

\(\frac{18.113}{63}=\frac{9\cdot2\cdot113}{9\cdot7}=\frac{2\cdot113}{7}=\frac{226}{7}\)

Kết quả là \(\frac{226}{7}\)

Đúng thì tk nha!!!

Để mình giúp bạn nha !!!

A) \(\frac{7}{15}\)

B) 4,391

\(18.\frac{113}{63}\)

\(=\frac{226}{7}\)

k mk nha mk nhanh nhất

Đây là tính nhanh nha bạn

Mình làm như câu hỏi trên rồi đó!

   \(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)

\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)

\(=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\right)\)

\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)

\(=\frac{1}{2}.\left(1-\frac{1}{15}\right)\)

\(=\frac{1}{2}.\frac{14}{15}\)

\(=\frac{7}{15}\)

a) \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)

\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{15}\right)=\frac{1}{2}.\frac{14}{15}\)\(=\frac{7}{15}\)

b)\(\frac{1414+1515+...+1919}{2020+2121+...+2525}\)

\(\Rightarrow\frac{101\left(14+15+16+17+18+19\right)}{101\left(20+21+22+23+24+25\right)}\)

\(=\frac{14+15+16+17+18+19}{20+21+22+23+24+25}\)

\(=\frac{\left(19+14\right).6:2}{\left(25+20\right).6:2}=\frac{19+14}{25+20}=\frac{33}{45}=\frac{11}{15}\)

\(\frac{1414+1515+1616+1717+1818+1919}{2020+2121+2222+2323+2424+2525}=\frac{9999}{13635}=\frac{11}{15}\)

Ai làm đúng và nhanh nhất mk k cho

cái thứ hai lớn hơn

Ta có : \(\frac{1212+1313+1414+1515+1616}{1717+1818+1919+2020+2121}=\frac{12+13+14+15+16}{17+18+19+20+21}=\frac{28\cdot\frac{5}{2}}{38\cdot\frac{5}{2}}=\frac{14}{19}\)

Dễ thấy \(\frac{111111}{666665}< \frac{1}{2}\) ( do 111111 < 666665/2 ) và \(\frac{14}{19}>\frac{1}{2}\) ( do 14 > 19/2 )

Vậy \(\frac{111111}{666665}< \frac{1212+1313+1414+1515+1616}{1717+1818+1919+2020+2121}\)

1.

a + b + c = 0 \(\Rightarrow\)a = - ( b + c ) \(\Rightarrow\)a² = [ -( b + c ) ]² \(\Rightarrow\)a² = b² + c² + 2bc

Tương tự : b² = a² + c² + 2ac ; c² = a² + b² + 2ab

a + b + c = 0 \(\Rightarrow\)a³ + b³ + c³ = 3abc  ( chứng minh )

Ta có : \(A=\frac{a^2}{b^2+c^2+2bc-b^2-c^2}+\frac{b^2}{a^2+c^2+2ac-a^2-c^2}+\frac{c^2}{a^2+b^2+2ab-a^2-b^2}\)

\(A=\frac{a^2}{2bc}+\frac{b^2}{2ac}+\frac{c^2}{2ab}\)

\(A=\frac{a^3+b^3+c^3}{2abc}=\frac{3abc}{2abc}=\frac{3}{2}\)

2. quy đồng mà giải

tại sao a+b+c=0 lại suy ra đc \(a^3+b^3+c^3=3abc\)