Question

If $a^2+b^2+c^2=250$ and $ab+bc+ca=3$, then find $a+b+c$.

Answer 1

$a^2+b^2+c^2=250$ & $ab+bc+ac=3$, find $a+b+c$

$\to$ the general formula

$(a+b+c{)}^2=a^2+b^2+c^2+2(ab+bc+ac)$

$=250+2\left(3\right)$

$=250+6$

$\therefore (a+b+c{)}^2=256$

$\therefore a+b+c=\sqrt{256}$

$\therefore a+b+c=16$