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So sánh 6262 / 7878 và 2424 / 3636
Vì 6262/7878 > 2424/3636
Nên 1414 + 1515 + 1616 + 1717 / 1818 + 1919 + 2020 + 2121 > 2424/3636
1414+1515+1616+1717+1818+1919/2020+2121+2222+2323+2424+2525
=14.101+15.101+16.101+17.101+18.101+19.101/20.101+21.101+22.101+23.101+24.101+25.101
=14+15+16+17+18+19/20+21+22+23+24+25
=99/135
=11/15
\(\frac{1414+1515+1616+1717+1818+1919}{2020+2121+2222+2323+2424+2525}\)
\(=\frac{101\left(14+15+16+17+18+19\right)}{101\left(20+21+22+23+24+25\right)}\)
\(=\frac{\left(19+14\right)\left(19-14+1\right):2}{\left(25+20\right)\left(25-20+1\right):2}\)
=\(\frac{33.6:2}{45.6:2}=\frac{33}{45}=\frac{11}{15}\)
a ) − 1212 − 2424 = ( − 1212 ) : ( − 1212 ) ( − 2424 ) : ( − 1212 ) = 1 2
b ) 120120 − 240240 = 120120 : ( − 120120 ) − 240240 : ( − 120120 ) = − 1 2
c) 1313 − 1414 = 1313 : ( − 101 ) − 1414 : ( − 101 ) = − 13 14
1414+1515+1616+1717+1818+1919/2020+2021+2222+2323+2424+2525
=14.101+15.101+16.101+17.101+18.101+19.101/20.101+21.101+22.101+23.101+24.101+25.101
=14+15+16+17+18+19/20+21+22+23+24+25
=99/135
=11/15
a) 33 66 = 33 : 33 66 : 33 = 1 2 b ) − 22 77 = − 22 : 11 77 : 11 = − 2 7
c ) 3030 6060 = 3030 : 3030 6060 : 3030 = − 1 2 d ) − 1212 − 2424 = ( − 1212 ) : ( − 1212 ) ( − 2424 ) : ( − 1212 ) = 1 2
e ) 120120 − 240240 = 120120 : ( − 120120 ) − 240240 : ( − 120120 ) = − 1 2
f ) 1313 − 1414 = 1313 : ( − 101 ) − 1414 : ( − 101 ) = − 13 14
Bài 2:
a) \(A=\frac{10n}{5n-3}=\frac{2\left(5n-3\right)+6}{5n-3}=2+\frac{6}{5n-3}\)
Vậy để A nguyên thì \(5n-3\inƯ\left(6\right)\)
Mà Ư(6)={1;-1;2;-2;3;-3;6;-6}
=>5n-3={1;-1;2;-2;3;-3;6;-6}
Ta có bảng sau:
5n-3 | 1 | -1 | 2 | -2 | 3 | -3 | 6 | -6 |
n | \(\frac{4}{5}\) | \(\frac{2}{5}\) | 1 | \(\frac{1}{5}\) | \(\frac{6}{5}\) | 0 | \(\frac{9}{5}\) | -\(\frac{3}{5}\) |
Vậy \(x=\left\{\frac{4}{5};\frac{2}{5};1;\frac{1}{5};\frac{6}{5};0;\frac{9}{5};-\frac{3}{5}\right\}\) thì A nguyên