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a) \(7^8+7^9+7^{10}\)
\(=7^8\left(1+7+7^2\right)\)
\(=7^8.57⋮57\)
b) \(10^{10}-10^9-10^8=10^8\left(10^2-10-1\right)\)
\(=10^8⋮89\)
\(\frac{5}{9}\cdot\frac{7}{13}+\frac{5}{9}\cdot\frac{9}{13}+\frac{3}{13}\cdot\left(-\frac{5}{9}\right)\)
\(=\frac{5}{9}\cdot\frac{7}{13}+\frac{5}{9}\cdot\frac{9}{13}-\frac{3}{13}\cdot\frac{5}{9}\)
\(=\frac{5}{9}\cdot\left(\frac{7}{13}+\frac{9}{13}-\frac{3}{13}\right)\)
\(=\frac{5}{9}\)
\(\frac{-24}{12}=\frac{x}{5}=\frac{-y}{3}=\frac{-z}{17}=\frac{t}{9}\)
\(\Rightarrow\frac{-24}{12}=\frac{x}{5}\Rightarrow12.x=-120\Rightarrow x=-10\)
\(\Rightarrow\frac{-24}{12}=\frac{-y}{3}\Rightarrow-12.y=-72\Rightarrow y=6\)
\(\frac{-24}{12}=\frac{-z}{17}\Rightarrow-12.z=-408\Rightarrow z=34\)
\(\Rightarrow\frac{-24}{12}=\frac{t}{9}\Rightarrow12.t=-216\Rightarrow t=-18\)
VẬY \(x=-10;y=6;z=34;t=-18\)
Ta có thể thấy:
\(\frac{11}{29};\frac{9}{17};\frac{10}{19}< \frac{2}{3}\)
\(\Rightarrow\frac{11}{29}+\frac{9}{17}+\frac{10}{19}< 3\times\frac{2}{3}=2\)
Chúc bn hok tốt
a)1.2.3.4...9-1.2.3.4...8-1.2.3.4...8.8
=1.2.3.4...8(9-1-8)
=1.2.3.4...8.0
=0
b)(3.4.216)2/11.123.411-169=(3.22.216)2/11.213.222-236=32.24.232/11.235-236=32.226/235.(11-2)
=32.236/235.9=32.236/235.32=2
c)70.(131313/565656+131313/727272+131313/909090
=70.(13/56+13/72+13/90)
=70.39/70=39
d)1/4.9+1/9.14+1/14.19+...+1/64.69
=4/4.9.4+4/9.4.14+4/14.19.4+...+4/64.69.4.
=1/4.(4/4.9+4/9.14+4/14.19+...+4/64.69)
=1/4.(1/4-1/9+1/9-1/14+1/14-1/19+...+1/64-1/69)
=1/4.(1/4-1/69)
=1/4.65/276=65/1104
~~~~~~~~Chúc bạn học giỏi nhé !~~~~~~~~
111111111
12345679 x9=111111111