Question

if a^2+b^2+c^2=74 and ab+bc+ca=61, Find a+b+c

Answer 1

Answer:

The answer is 14 or -14

Step-by-step explanation:

Given $a^2+b^2+c^2=74$ and $ab+bc+ca=61$

We know the identity,  $(a+b+c)^2=a^2+b^2=c^2+2(ab+bc+ca)$

$\Rightarrow (a+b+c)^2=74+2(61)=74+122=196$, by substituting the given values

$\Rightarrow a+b+c=\pm\sqrt{196}=\pm 14$