If a² + b² + c² = 90 and a + b + c = 20 then find the value of ab + bc + ca.

Given: a² + b² + c² = 90 and a + b + c = 20

To find: ab + bc + ca

Using formula:

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

Substituting the values of a + b + c = 20 and a² + b² + c² = 90 in the given formula, we have,

(20)² = 90 + 2(ab + bc + ca)

400 = 90 + 2(ab + bc + ca)

310 = 2(ab + bc + ca)

ab + bc + ca = 155