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Question

So sánh A = $\dfrac{3^{10}+1}{3^9+1}$                      và                          B = $\dfrac{3^9+1}{3^8+1}$

Nguyễn Lê Phước Thịnh · Accepted Answer

Ta có: $A=\dfrac{3^{10}+1}{3^9+1}$$\Leftrightarrow A=\dfrac{3^{10}+3-2}{3^9+1}$hay $A=3-\dfrac{2}{3^9+1}$Ta có: $B=\dfrac{3^9+1}{3^8+1}$$\Leftrightarrow B=\dfrac{3^9+3-2}{3^8+1}$hay $B=3-\dfrac{2}{3^8+1}$Ta có: $3^9+1>3^8+1$$\Leftrightarrow\dfrac{2}{3^9+1}< \dfrac{2}{3^8+1}$$\Leftrightarrow-\dfrac{2}{3^9+1}>-\dfrac{2}{3^8+1}$$\Leftrightarrow-\dfrac{2}{3^9+1}+3>-\dfrac{2}{3^8+1}+3$hay A>BCâu trả lời: Ta có: $A=\dfrac{3^{10}+1}{3^9+1}$$\Leftrightarrow A=\dfrac{3^{10}+3-2}{3^9+1}$hay $A=3-\dfrac{2}{3^9+1}$Ta có: $B=\dfrac{3^9+1}{3^8+1}$$\Leftrightarrow B=\dfrac{3^9+3-2}{3^8+1}$hay $B=3-\dfrac{2}{3^8+1}$Ta có: $3^9+1>3^8+1$$\Leftrightarrow\dfrac{2}{3^9+1}< \dfrac{2}{3^8+1}$$\Leftrightarrow-\dfrac{2}{3^9+1}>-\dfrac{2}{3^8+1}$$\Leftrightarrow-\dfrac{2}{3^9+1}+3>-\dfrac{2}{3^8+1}+3$hay A>B

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