720 : [41 - (2x - 5)] = 22 . 5
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A=(7+73).(1+7+72+73+..+79)
=350.B
Vì 350 chia hết cho 10 nên A chia hết cho 10
=
Lời giải:
$x+(x+1)+(x+2)+.....+(x+49)+50+51=1776$
$[\underbrace{(x+x+....+x)}_{50}+(1+2+3+....+49)]+50+51=1776$
$x\times 50+(1+2+3+....+50+51)+1776$
$x\times 50+51\times 52:2=1776$
$x\times 50+1326=1776$
$x\times 50=450$
$x=450:50=9$
Đặt: \(A=9^9+9^{10}+...+9^{20}\)
\(9A=9\cdot\left(9^9+9^{10}+...+9^{20}\right)\)
\(9A=9^{10}+9^{11}+...+9^{21}\)
\(9A-A=9^{10}+9^{11}+...+9^{21}-9^9-9^{10}-...-9^{20}\)
\(8A=9^{21}-9^9\)
\(A=\dfrac{9^{21}-9^9}{8}\)
\(4\cdot5^2-3\cdot2^3+3^3\cdot3^2\)
\(=4\cdot25-3\cdot8+3^{2+3}\)
\(=100-24+3^5\)
\(=100-24+243\)
\(=343-24\)
\(=319\)
3n + 5 chia hết cho 2n + 1
⇒ 2(3n + 5) chia hết cho 2n + 1
⇒ 6n + 10 chia hết cho 2n + 1
⇒ 6n + 3 + 7 chia hết cho 2n + 1
⇒ 3(2n + 1) + 7 chia hết cho 2n + 1
⇒ 7 chia hết cho 2n + 1
⇒ 2n + 1 ∈ Ư(7) = {1; -1; 7; -7}
⇒ n ∈ {0; -1; 3; -4}
Mà: n ∈ N
⇒ n ∈ {0; 3}
\(A=24\cdot6^3\)
\(A=4\cdot6\cdot\left(2\cdot3\right)^3\)
\(A=2^2\cdot2\cdot3\cdot2^3\cdot3^3\)
\(A=\left(2^2\cdot2\cdot2^3\right)\cdot\left(3\cdot3^3\right)\)
\(A=2^6\cdot3^4\)
\(A=2+2^2+...+2^{60}\)
\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{59}+2^{60}\right)\)
\(A=2\cdot3+2^3\cdot3+...+2^{59}\cdot3\)
\(A=3\cdot\left(2+2^3+...+2^{59}\right)\)
Vậy A chia hết cho 3
_______________
\(A=2+2^2+2^3+...+2^{60}\)
\(A=\left(2+2^3\right)+\left(2^2+2^4\right)+...+\left(2^{58}+2^{60}\right)\)
\(A=2\cdot5+2^2\cdot5+...+2^{58}\cdot5\)
\(A=5\cdot\left(2+2^2+...+2^{58}\right)\)
Vậy A ⋮ 5
___________________
\(A=2+2^2+2^3+...+2^{60}\)
\(A=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{58}+2^{59}+2^{60}\right)\)
\(A=2\cdot7+2^4\cdot7+...+2^{58}\cdot7\)
\(A=7\cdot\left(2+2^4+...+2^{58}\right)\)
Vậy A ⋮ 7
\(24\cdot\left(x-16\right)=144\)
\(\Rightarrow x-16=\dfrac{114}{24}\)
\(\Rightarrow x-16=6\)
\(\Rightarrow x=6+16\)
\(\Rightarrow x=22\)
Vậy: \(x=22\)
24 . ( x - 16 ) = 144
( x - 16 ) = 144 : 24
x - 16 = 6
x. = 6 + 16
x. = 22
\(720:\left[41-\left(2x-5\right)\right]=2^2.5\\ =>720:\left(41-2x+5\right)=4.5=20\\ =>46-2x=720:20=36\\ =>2x=46-36=10\\ =>x=5\)
\(720:\left[41-\left(2x-5\right)\right]=2^2\cdot5\)
\(\Rightarrow720:\left[41-\left(2x-5\right)\right]=4\cdot5\)
\(\Rightarrow720:\left[41-\left(2x-5\right)\right]=20\)
\(\Rightarrow41-\left(2x-5\right)=720:20\)
\(\Rightarrow41-\left(2x-5\right)=36\)
\(\Rightarrow2x-5=41-36\)
\(\Rightarrow2x-5=5\)
\(\Rightarrow2x=5+5\)
\(\Rightarrow2x=10\)
\(\Rightarrow x=\dfrac{10}{2}\)
\(\Rightarrow x=5\)