Question

If a + b+ c =8, a2 +b2 + c2 = 30. Find the value of a b + b c + c a​

Answer 1

Step-by-step explanation:

a + b + c = 8

Doing square both side

(a + b + c)² = 64

a² + b² + c² + 2(ab + bc + ca) = 64

30 + 2(ab + bc + ca) = 64

2(ab + bc + ca) = 34

ab + bc + ca = 17

Answer 2

Answer:

17

Step-by-step explanation:

Given that,

$a + b + c = 8$

And

${a}^{2} + {b}^{2} + {c}^{2} = 30$

To find the value of (ab + bc + ca)

We know that,

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

Substituting the values, we get,

$= > {8}^{2} = 30 + 2(ab + bc + ca) \\ \\ = > 2(ab + bc + ca) + 30 = 64 \\ \\ = > 2(ab + bc + ca) = 64 - 30 \\ \\ = > 2(ab + bc + ca) = 34 \\ \\ = > ab + bc + ca = \frac{34}{2} \\ \\ = > ab + bc + ca = 17$

Hence, the required value of (ab+bc+ca) is 17.