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\(A=\dfrac{10^9+1}{10^{10}+1}>B=\dfrac{10^8+1}{10^9+1}\)

\(42\cdot53+47\cdot186-114\cdot47\)

\(=42\cdot53+47\cdot\left(186-114\right)\)

\(=42\cdot53+47\cdot72\)

\(=2226+3384\)

\(=5610\)

42.53 + 47.186 - 114.47

= 2226 + 47.(186 - 114)

= 2226 + 47. 72

= 2226 + 3384 = 5610

các chữ cái có tâm đối xứng là: A, H, I, M, O, T, U, V, W, X, và Y

Y,H,N,S,X,Z,...

   A     =  1 + 2² + 2³ + ...+ 2²⁰¹²

2.A    =  2  + 2³+ 2⁴ +...+ 2²⁰¹³

2A - A = 2 + 2²+ 2³ + 2⁴ +...+ 2²⁰¹³ - (1 + 2² + 2³ + ... + 2²⁰¹²)

A = 2 + 2² + 2⁴ + ..  + 2²⁰¹³  - 1 - 2² - 2³ -...- 2²⁰¹²

A = (2 - 2²) + (2³ - 2³) +  (2⁴ - 2⁴) + (2⁵ - 2⁵) + (2²⁰¹² - 2²⁰¹²) + (2²⁰¹³ - 1)

A = -2 + 0 +...+ 0 + 2²⁰¹³ - 1

A = 2²⁰¹³  - 3

Ban trả lời đúng là thần đồng

\(\dfrac{3-x}{5}\) = \(\dfrac{6}{11}\)

3 - \(x\) = \(\dfrac{6}{11}\).5

3 - \(x\) = \(\dfrac{30}{11}\)

     \(x\) = 3 - \(\dfrac{30}{11}\) 

    \(x\) =  \(\dfrac{3}{11}\)

\(\dfrac{3-x}{5}=\dfrac{6}{11}\)

\(3-x=\dfrac{6}{11}\cdot5\)

\(3-x=\dfrac{30}{11}\)

\(x=3-\dfrac{30}{11}\)

\(x=\dfrac{3}{11}\)

\(\dfrac{-4}{8}\) = \(\dfrac{x}{-10}\) ⇒ \(x\) =  - \(\dfrac{4}{8}\).(-10) = 5

y =  -7 : (\(-\dfrac{4}{8}\)) = 14

z = -\(\dfrac{4}{8}\) \(\times\) (-24) = 12

Vậy (\(x;y;z\)) = (5; 14; 12)

\(\left(x;y;z\right)=\left(5;14;12\right)\)

7�+1n+17​ là số nguyên nếu $n$ là số nguyên.

      \(\dfrac{-4}{11}\) = \(\dfrac{x}{22}\) = \(\dfrac{40}{y}\)

         \(x\) = -\(\dfrac{4}{11}\).22 = -8

         y = 40 :( -\(\dfrac{4}{11}\))

          y = - 110

Vậy (\(x\);y) =(-8; -110)

\(\dfrac{-4}{11}=\dfrac{x}{22}=\dfrac{40}{y}\)

\(\Rightarrow\dfrac{-4}{11}=\dfrac{x}{22}\)

\(\Rightarrow\dfrac{-4}{11}=\dfrac{-4\cdot2}{11\cdot2}=\dfrac{-8}{22}\)

\(\Rightarrow\dfrac{-8}{22}=\dfrac{40}{y}\)

\(\Rightarrow\dfrac{-8}{22}=\dfrac{-8\cdot\left(-5\right)}{22\cdot\left(-5\right)}=\dfrac{40}{-110}\)

\(\Rightarrow\dfrac{-4}{11}=\dfrac{-8}{22}=\dfrac{40}{-110}\)

\(\Rightarrow\left(x,y\right)=\left(-8;-110\right)\)

\(3-\left(\dfrac{1}{6}-x\right)\times\dfrac{2}{3}=\dfrac{2}{3}\)

\(\left(\dfrac{1}{6}-x\right)\times\dfrac{2}{3}=3-\dfrac{2}{3}\)

\(\left(\dfrac{1}{6}-x\right)\times\dfrac{2}{3}=\dfrac{7}{3}\)

\(\dfrac{1}{6}-x=\dfrac{7}{3}:\dfrac{2}{3}\)

\(\dfrac{1}{6}-x=\dfrac{7}{3}\times\dfrac{3}{2}\)

\(\dfrac{1}{6}-x=\dfrac{21}{6}\)

\(\dfrac{1}{6}-x=\dfrac{7}{2}\)

\(x=\dfrac{1}{6}-\dfrac{7}{2}\)

\(x=\dfrac{1}{6}-\dfrac{21}{6}\)

\(x=\dfrac{-20}{6}\)