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

9

Step-by-step 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