If $a^{2} + b^{2} + c^{2} = 50$ and $ab + bc + ca = 47$, find $a + b + c$ (positive value).

If $a^{2} + b^{2} + c^{2} = 50$ and $ab + bc + ca = 47$, find $a + b + c$ (positive value).
  1. $12$
  2. $10$
  3. $8$
  4. $14$

Solution

$(a+b+c)^{2} = a^{2}+b^{2}+c^{2} + 2(ab+bc+ca) = 50 + 94 = 144$. So $a+b+c = 12$.

Asked in: IMO

Practice more ALGEBRAIC EXPRESSIONS AND IDENTITIES questions on Aicharya