Question

If a+b+c=7 and ab+bc+ca=20 find the value of a^2+b^2+c^2

Answer 1

9

Explanation:

Using the identity

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

Subtract 2(ab + bc + ca) from both sides, then

a² + b² + c² = (a + b + c)² - 2(ab + bc + ca) = 7² - 2(20) = 49 - 40 = 9