Question:
If \[ a^2+b^2+c^2=24 \] and \[ ab+bc+ca=-4 \] find:
\[ a+b+c \]
Solution:
Using identity:
\[ (a+b+c)^2 = a^2+b^2+c^2+2(ab+bc+ca) \]
Substituting the given values:
\[ (a+b+c)^2 = 24+2(-4) \]
\[ = 24-8 \]
\[ =16 \]
\[ a+b+c = \sqrt{16} \]
\[ =\pm4 \]