HSG toán

V

vancoi999

Last edited by a moderator:
H

huynhbachkhoa23

$\sqrt{(a+b+c)(a'+b'+c')}=\sqrt{aa'}+\sqrt{bb'}+ \sqrt{cc'}\leftrightarrow (a+b+c)(a'+b'+c')=aa'+bb'+cc'+2\sqrt{aa'bb'}+ 2\sqrt{bb'cc'}+2\sqrt{cc'aa'}$
$\leftrightarrow a(b'+c')+b(c'+a')+c(a'+b')=2\sqrt{aa'bb'}+2\sqrt{bb'cc'}+2\sqrt{cc'aa'}$
$\leftrightarrow (\sqrt{b'c}-\sqrt{bc'})^2+(\sqrt{c'a}-\sqrt{ca'})^2+(\sqrt{a'b}-\sqrt{ab'})^2=0 \leftrightarrow \dfrac{a}{a'}=\dfrac{b}{b'}=\dfrac{c}{c'}$
 
You must log in or register to reply here.
Top Bottom