So sánh \(A = \frac{{{{20}^{10}} + 1}}{{{{20}^{10}} - 1}}\) và \(B = \frac{{{{20}^{10}} - 1}}{{{{20}^{10}} - 3}}\)
\(\begin{array}{l}
A = \frac{{{{20}^{10}} + 1}}{{{{20}^{10}} - 1}} = 1\frac{2}{{{{20}^{10}} - 1}}\left( 1 \right)\\
B = \frac{{{{20}^{10}} - 1}}{{{{20}^{10}} - 3}} = 1\frac{2}{{{{20}^{10}} - 3}}\left( 2 \right)
\end{array}\)
Vì \(\frac{2}{{{{20}^{10}} - 1}} < \frac{2}{{{{20}^{10}} - 3}}\left( 3 \right)\)
Nên từ (1), (2) và (3) suy ra A < B
-- Mod Toán 6
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