hi sinh sớm thế

\(\frac{3}{4}\) lít dầu hỏa cân nặng \(\frac{41}{50}-\frac{1}{4}=\frac{57}{100}\) (kg)

Mỗi lít dầu hỏa cân nặng \(\frac{3}{4}:\frac{57}{100}=\frac{25}{19}\) (kg)

Gọi d là ƯCLN(n + 1,3n + 4)

\(\Rightarrow\left\{{}\begin{matrix}n+1⋮d\\3n+4⋮d\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}3n+3⋮d\\3n+4⋮d\end{matrix}\right.\)

\(\Rightarrow\left(3n+4\right)-\left(3n+3\right)⋮d\)

\(\Rightarrow3n+4-3n-3⋮d\Rightarrow1⋮d\)

\(\Rightarrow\)ƯCLN(n + 1,3n + 4) = 1

Vậy n + 1 và 3n + 4 là hai số nguyên tố cùng nhau

\(\dfrac{1}{4}.\dfrac{2}{6}.\dfrac{3}{8}.\dfrac{4}{10}.\dfrac{5}{12}.....\dfrac{30}{62}.\dfrac{31}{64}=2x\)

\(\dfrac{1.2.3.4.5.....30.31}{\left(2.2\right)\left(2.3\right)\left(2.4\right)\left(2.5\right)\left(2.6\right).....\left(2.31\right)\left(2.32\right)}=2x\)

\(\dfrac{1\left(2.3.4.5....30.31\right)}{32\left(2.3.4.5.....31\right).2^{31}}=2x\)

\(\dfrac{1}{2^5.2^{31}}=2x\Rightarrow2x=\dfrac{1}{2^{36}}\Rightarrow x=\dfrac{1}{2^{36}}\div2=\dfrac{1}{2^{37}}\)

Vậy x = \(\dfrac{1}{2^{37}}\)