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[SlowMind]

Cho tam giác ABC, $\widehat{A}=2\widehat{B}$. Cm $BC ^2 = AC ^2 + AC.AB.$

Edited by tpdtthltvp, 30-05-2016 - 09:09.

[quanminhanh]

$\frac{BC}{\ sin \hat {A}} = \frac{AC}{\ sin \hat {B}} \Leftrightarrow \frac{BC}{\ sin 2 \widehat{B}} = \frac{AC}{\sin \widehat {B}} \Leftrightarrow \frac {BC}{2 \ cos \widehat {B}} = AC \Leftrightarrow BC = AC \cdot \frac {AC ^ {2} + BC ^ { 2} -AC ^ {2}} {AB \cdot BC} \Leftrightarrow AB \cdot BC ^ {2} = AB ^ {2} \cdot AC + AC \cdot BC ^ {2} -AC ^ {3} \Leftrightarrow BC ^ {2} (AB-AC) = AC (AB-AC) (AB + AC) \Leftrightarrow BC ^{2} = AC ^ {2} + AB \cdot AC$

 

P/S: nhớ like cho mình để thăng cấp nhé

Edited by tpdtthltvp, 30-05-2016 - 12:29.