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\(a.\)
\(A=\)\(\frac{10^{15}+1}{10^{16}+1}\)
\(10A=\) \(\frac{10\left(10^{15}+1\right)}{10^{16}+1}\)
\(10A=\) \(\frac{10^{16}+10}{10^{16}+1}\)
\(10A=\)\(\frac{10^{16}+1+9}{10^{16}+1}\)
\(10A=\frac{10^{16}+1}{10^{16}+1}+\frac{9}{10^{16}+1}\)
\(10A=1+\frac{9}{10^{16}+1}\)
\(B=\frac{10^{16}+1}{10^{17}+1}\)
\(10B=\frac{10\left(10^{16}+1\right)}{10^{17}+1}\)
\(10B=\frac{10^{17}+10}{10^{17}+1}\)
\(10B=\frac{10^{17}+1+9}{10^{17}+1}\)
\(10B=\frac{10^{17}+1}{10^{17}+1}+\frac{9}{10^{17}+1}\)
\(10B=1+\frac{9}{10^{17}+1}\)
\(\Rightarrow10B< 10A\Rightarrow B< A\)\(\text{( vì tự làm ) }\)
xin lỗi hôm qua mk đang làm thì phải đy học zoom học xong quên h mới nhơ ra làm típ :)
b
\(A=\frac{3}{8^3}+\frac{7}{8^4}=\frac{3}{8^3}+\frac{3}{8^4}+\frac{4}{8^4}\)
\(B=\frac{3}{8^4}+\frac{7}{8^3}=\frac{3}{8^4}+\frac{3}{8^3}+\frac{4}{8^3}\)
Vì \(\frac{4}{8^4}< \frac{4}{8^3}\)=.> A < B
j) \(\frac{8}{3}.\frac{2}{5}.\frac{3}{8}.10.\frac{19}{92}=\left(\frac{8}{3}.\frac{3}{8}\right).\left(\frac{2}{5}.10\right).\frac{19}{92}=1.4.\frac{19}{92}\)
\(=\frac{19}{23}\)
k)\(\frac{-5}{7}.\frac{2}{11}.\frac{-13}{17}.\frac{19}{12}.\frac{17}{13}=\left(\frac{2}{11}.\frac{19}{12}\right).\left(\frac{-13}{17}.\frac{17}{13}\right).\frac{-5}{7}\)
\(=\frac{-19}{66}.\frac{-5}{7}=\frac{95}{462}\)
l)\(\frac{12}{19}.\frac{7}{15}.\frac{-13}{17}.\frac{19}{12}.\frac{17}{13}=\left(\frac{12}{19}.\frac{19}{12}\right).\left(\frac{-13}{17}.\frac{17}{13}\right).\frac{7}{15}\)
\(=\frac{-7}{15}\)
cậu tham khảo trên này ạ, nếu đúng cho mk 1 t.i.c.k ạ, thank nhiều
\(\frac{-8}{10}.\frac{74}{7}+\frac{17}{7}.\frac{-8}{13}+\frac{3}{5}=\frac{-8}{7}.\frac{37}{5}+\frac{-8}{7}.\frac{17}{13}+\frac{3}{5}\)
\(=\frac{-8}{7}.\left(\frac{37}{5}+\frac{17}{13}\right)+\frac{3}{5}=\frac{-8}{7}.\frac{566}{65}+\frac{3}{5}\)
\(=\frac{-4528}{455}+\frac{273}{455}=\frac{-4255}{455}=\frac{851}{91}\)
851/91