a là số tự nhiên lẻ nên a=2k+1

\(\left(a-1\right)\left(a+1\right)=\left(2k+1-1\right)\left(2k+1+1\right)\)

\(=2k\left(2k+2\right)=4k\left(k+1\right)\)

Vì k;k+1 là hai số tự nhiên liên tiếp

nên \(k\left(k+1\right)⋮2\)

=>\(4k\left(k+1\right)⋮8\)

=>\(\left(a-1\right)\left(a+1\right)⋮8\left(1\right)\)

TH1: a=3n+1

\(\left(a-1\right)\left(a+1\right)=\left(3n+1-1\right)\left(3n+1+1\right)=3n\left(3n+2\right)⋮3\)(2)

TH2: a=3n+2

\(\left(a-1\right)\left(a+1\right)=\left(3n+2-1\right)\left(3n+2+1\right)\)

\(=\left(3n+3\right)\left(3n+1\right)=3\left(n+1\right)\left(3n+1\right)⋮3\left(3\right)\)

Từ (2),(3) suy ra \(\left(a-1\right)\left(a+1\right)⋮3\left(4\right)\)

Từ (1),(4) suy ra \(\left(a-1\right)\left(a+1\right)⋮BCNN\left(8;3\right)\)

=>\(\left(a-1\right)\left(a+1\right)⋮24\)

\(\dfrac{15}{2}\times\dfrac{18}{19}+\dfrac{15}{2}\times\dfrac{1}{19}\)

\(=\dfrac{15}{2}\times\left(\dfrac{18}{19}+\dfrac{1}{19}\right)\)

\(=\dfrac{15}{2}\times1\)

\(=\dfrac{15}{2}\)

11x9-900x0,1-9

=99-9-90

=0

b: TH1: n=3k+1

\(n^2+2006=\left(3k+1\right)^2+2006\)

\(=9k^2+6k+1+2006\)

\(=9k^2+6k+2007=3\left(3k^2+2k+669\right)⋮3\)(1)

TH2: n=3k+2

\(n^2+2006=\left(3k+2\right)^2+2006\)

\(=9k^2+12k+2010=3\left(3k^2+4k+670\right)⋮3\left(2\right)\)

Từ (1),(2) suy ra \(n^2+2006\) là hợp số

\(A=\dfrac{1}{1\cdot4}+\dfrac{1}{4\cdot7}+\dfrac{1}{7\cdot11}+\dfrac{1}{11\cdot14}+\dfrac{1}{14\cdot17}\)

\(=\dfrac{1}{3}\cdot\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot11}+\dfrac{3}{11\cdot14}+\dfrac{3}{14\cdot17}\right)\)

\(=\dfrac{1}{3}\cdot\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{17}\right)\)

\(=\dfrac{1}{3}\cdot\left(1-\dfrac{1}{17}\right)\)

\(=\dfrac{1}{3}\cdot\dfrac{16}{17}=\dfrac{16}{51}\)

cũng dễ

Số học sinh lớp 5b là:

57:100×59= 33,63( học sinh)

Số học sinh lớp 5A là:

57-33,63=23,37(học sinh)

Đáp số:5a:23,37 hs

5b:33,63 hs

bạn có sai đề ko số tôi tính ra số thập phân

28,567-76,27=(-47,703)

65,30+28,54=93,84

15*3,145=47.175

15*3,145=47,175