[Toán 7] Chứng minh

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thebooktheif

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nhuquynhdat

Từ $\dfrac{a}{b}=\dfrac{c}{d} \Longrightarrow \dfrac{a}{c}=\dfrac{b}{d} \Longrightarrow \dfrac{a^2}{c^2}=\dfrac{a}{c}.\dfrac{b}{d}=\dfrac{ab}{cd}$

$ \Longrightarrow \dfrac{7a^2}{7c^2}=\dfrac{3ab}{3cd}=\dfrac{7a^2+3ab}{7c^2+3cd} \Longrightarrow \dfrac{a^2}{c^2}=\dfrac{7a^2+3ab}{7c^2+3cd}$ (*)

Mặt khác, $ \dfrac{a^2}{c^2}=\dfrac{b^2}{d^2} \Longrightarrow \dfrac{11a^2}{11c^2}=\dfrac{8b^2}{8d^2} =\dfrac{11a^2-8b^2}{11c^2-8d^2}$

$\Longrightarrow \dfrac{a^2}{c^2}=\dfrac{11a^2-8b^2}{11c^2-8d^2}$ (*) (*)

Từ (*) và (*)(*) $\Longrightarrow \dfrac{7a^2+3ab}{7c^2+3cd}=\dfrac{11a^2-8b^2}{11c^2-8d^2} \Longrightarrow \dfrac{7a^2 + 3ab}{11a^2 - 8b^2}= \dfrac{7c^2 + 3cd}{11c^2 - 8d^2}$
 
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