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\(A=\frac{\left[\left(25-1\right):1+1\right]\left(25+1\right)}{2}=325.\)
\(B=\frac{\left[\left(51-3\right):2+1\right]\left(51+3\right)}{2}=675\)
\(C=\frac{\left[\left(81-1\right):4+1\right]\left(81+1\right)}{2}=861\)
\(2^4.5-\left[31-9^2\right]=16.5-\left(31-81\right)=80-\left(-50\right)=130\)
\(2^4\).5-[1.31-(13-4)^2]
=16.5-[1.31-81]
=16.5-[31-81]
=16.5-(-50)
=80-(-50)
=130
\(5.8^{x+3}+\left(194:26\right)^0=2561\)
\(\Rightarrow5.8^{x+3}=2561-1=2560\)
\(\Rightarrow8^{x+3}=2560:5=512=8^3\)
\(\Rightarrow x+3=3\Leftrightarrow x=0\)
5.8x+3 + (194:26)0 = 2561
5.8x. 512 + 1 = 2561
8x . 2560 = 2560
8x =1 = 80
=> x = 0
Lời giải:
$C=1+3^2+3^3+(3^4+3^5+3^6)+(3^7+3^8+3^9)+....+(3^{97}+3^{98}+3^{99})$
$=37+3^4(1+3+3^2)+3^7(1+3+3^2)+...+3^{97}(1+3+3^2)$
$=11+13.2+(1+3+3^2)(3^4+3^7+...+3^{97})$
$=11+13.2+13(3^4+3^7+...+3^{97})$
$=11+13(2+3^4+3^7+....+3^{97})$
$\Rightarrow C$ chia $13$ dư $11$.
Vì n-2 là Ư(3n-13) nên 3n-13 \(⋮\)n-2
=> n-2 \(⋮\)n-2
=> ( 3n-13) - (n-2) \(⋮\)n-2
=> (3n-13) - 3(n-2) \(⋮\)n-2
=> 3n-13 - 3n + 6 \(⋮\)n-2
=>7 \(⋮\)n-2
=> n-2 \(\in\)Ư(7)= {1;7; -1; -7}
=> n \(\in\){ 3; 9; 1; -5}
Vậy...
Ta có n - 2 là ước của 3n - 13
\(\Leftrightarrow3n-13⋮n-2\)
\(\Leftrightarrow3.\left(n-2\right)-7⋮n-2\)
\(\Leftrightarrow7⋮n-2\)
\(\Leftrightarrow n-2\in\left\{-7;-1;7;1\right\}\)
\(\Leftrightarrow\) \(n\in\left\{-5;1;9;3\right\}\)
Vậy \(n\in\left\{-5;1;9;3\right\}\)
Học tốt
2782 : [ 216 -( x-3) ]=13
=> 216 -( x-3) = 2782 : 13
=> 216 -(x-3) = 214
=> x-3 = 216 - 214
=> x-3 = 2
=> x = 5
Vậy x = 5
Chúc bạn học giỏi nhé
Nhớ k cho mk nha
a) \(\dfrac{13}{20}+\dfrac{3}{5}+x=\dfrac{5}{6}\)
\(\Rightarrow\dfrac{5}{4}+x=\dfrac{5}{6}\)
\(\Rightarrow x=\dfrac{5}{6}-\dfrac{5}{4}\)
\(\Rightarrow x=\dfrac{-5}{12}\)
b) \(x+\dfrac{1}{3}=\dfrac{2}{5}-\dfrac{-1}{3}\)
\(\Rightarrow x+\dfrac{1}{3}=\dfrac{11}{15}\)
\(\Rightarrow x=\dfrac{11}{15}-\dfrac{1}{3}\)
\(\Rightarrow x=\dfrac{2}{5}\)
c)\(\dfrac{-5}{8}-x=\dfrac{-3}{20}-\dfrac{-1}{6}\)
\(\dfrac{-5}{8}-x=\dfrac{1}{60}\)
\(\Rightarrow x=\dfrac{-5}{8}-\dfrac{1}{60}\)
\(\Rightarrow x=\dfrac{-77}{120}\)
d) \(\dfrac{3}{5}-x=\dfrac{1}{4}+\dfrac{7}{10}\)
\(\Rightarrow\dfrac{3}{5}-x=\dfrac{19}{20}\)
\(\Rightarrow x=\dfrac{3}{5}-\dfrac{19}{20}\)
\(\Rightarrow x=\dfrac{-7}{20}\)
e) \(\dfrac{-3}{7}-x=\dfrac{4}{5}+\dfrac{-2}{3}\)
\(\Rightarrow\dfrac{-3}{7}-x=\dfrac{2}{15}\)
\(\Rightarrow x=\dfrac{-3}{7}-\dfrac{2}{15}\)
\(\Rightarrow x=\dfrac{-59}{105}\)
g) \(\dfrac{-5}{6}-x=\dfrac{7}{12}+\dfrac{-1}{3}\)
\(\Rightarrow\dfrac{-5}{6}-x=\dfrac{1}{4}\)
\(\Rightarrow x=\dfrac{-5}{6}-\dfrac{1}{4}\)
\(\Rightarrow x=\dfrac{-13}{12}\)
(3.4x-5.122):13 = 12
3.4x-5.144 = 156
432.4x-5 = 156
4x-5 = 13/36
4x : 45 = 13/36
4x = 13/36864
...