Question

Cho tam giác abc cmr nếu ab^2 + ac^2 - ac.ac = bc^2 thì góc a = 60 độ.

Answer 1

Xét ΔABC có 

\(cosA=\dfrac{AB^2+AC^2-BC^2}{2\cdot AB\cdot AC}\)

=>\(\dfrac{AB^2+AC^2-BC^2}{2\cdot AB\cdot AC}=cos60=\dfrac{1}{2}\)

=>\(AB^2+AC^2-BC^2=AB\cdot AC\)

=>\(AB^2+AC^2-AB\cdot AC=BC^2\)(ĐPCM)