Question

If a² + b² + c² = 65 and ab + bc + ca = 8, find the value of a + b + c.

Answer 1

Here, a² + b² + c² = 65 and ab + bc + ca = 8,

Using the identity:

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

(a + b + c)² = 65 + 2(8)

(a + b + c)² = 65 + 16

(a + b + c)² = 81

a + b + c = `sqrt81`

∴ a + b + c = ±9