\(\left(1-\dfrac{1}{1+2}\right)\left(1-\dfrac{1}{1+2+3}\right)...\left(1-\dfrac{1}{1+2+3+...+1986}\right)\)

Tìm x,y và z

\(\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}\)

\(\dfrac{x-3}{4}=\dfrac{y}{15};\dfrac{y}{10}=\dfrac{z+7}{7}\)

Cho tỉ lệ thức \(\dfrac{a}{b}=\dfrac{c}{d}\). Hãy chứng minh rằng :

\(\dfrac{a}{a+b}=\dfrac{c}{c+d}\)

\(\dfrac{a+2c}{b+2d}=\dfrac{a-2c}{b-2d}\)

\(\dfrac{a^2+2b^2}{c^2+2d^2}=\dfrac{a^2-2b^2}{c^2-2d^2}\)

\(\dfrac{ab}{cd}=\dfrac{\left(a+b\right)^2}{\left(c+d\right)^2}\)

Tìm x,y biết :

\(\dfrac{x}{4}=\dfrac{y}{6}\) và xy =24