Question

If a2 +b2 +c2 = 105 and ab+ bc + ca = 92, find the value of a+b+c

Answer 1

Answer:

a + b + c = 17

Step-by-step explanation:

${a}^{2} + {b}^{2} + {c}^{2} = 105$

$ab + bc + ac = 92$

We know the algebraic identity,

${(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ac)$

By applying the given values,

${(a + b + c)}^{2} = 105 + 184 = 289$

$a + b + c = \sqrt{289} = 17$