Question

If a² + b² + c² = 26 and a + b + c = 8, find the value of ab + bc + ca.

Answer 1

Here, a² + b² + c² = 26 and a + b + c = 8,

Using the identity:

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

(8)² = 26 + 2(ab + bc + ca)

64 = 26 + 2(ab + bc + ca)

2(ab + bc + ca) = 64 − 26

2(ab + bc + ca) = 38

ab + bc + ca = `38/2`

∴ ab + bc + ca = 19