Question

If a² + b² + c² = 16 and ab + bc + ca = 10, find the value of a + b + c.

Answer 1

We know that,

${\displaystyle {(a+b+c)}^2=a^2+b^2+c^2+2(ab+bc+ca)}$

${\displaystyle \Rightarrow {(a+b+c)}^2=16+2\left(10\right)}$      [${\displaystyle \because a^2+b^2+c^2=16}$ and ab + bc + ca = 10]

${\displaystyle \Rightarrow {(a+b+c)}^2=16+20}$

${\displaystyle \Rightarrow (a+b+c)=\sqrt{36}}$

${\displaystyle \Rightarrow a+b+c=\pm 6}$