If a² + b² + c² = 250 and ab + bc + ca = 3, Find a + b + c

Solution

We know that

\[ (a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca) \]

Substituting the given values:

\[ (a+b+c)^2=250+2(3) \]

\[ (a+b+c)^2=250+6 \]

\[ (a+b+c)^2=256 \]

Taking square root:

\[ a+b+c=\pm16 \]

Therefore,

\[ \boxed{a+b+c=\pm16} \]