Question

Determinati aria tringhiului ale carui laturi verifica relatia
$a^{2}+ b^{2}+ c^{2} +6=2(c \sqrt{3}+b \sqrt{2}+a)$

Answer 1

$( a^{2}-2a+1)+( b^{2}-2 b\sqrt{2}+2)+( c^{2}-2c \sqrt{3}+3)=0 \\ (a-1)^2+(b- \sqrt{2})^2+(c- \sqrt{3})^2=0 \\ a=1;b= \sqrt{2};c= \sqrt{3}$
deci triunghiul este dreptunghic cu catetele a=1;b=√2 si ipotenuza c=√3
A=$\frac{ab}{2}= \frac{1* \sqrt{2} }{2}= \frac{ \sqrt{2} }{2}$