If a + b + c = 9 and ab + bc + ca = 26 find the value of a^2 + b^2 + c^2.
To start this problem, we will first square (a+b+c). This will be, in expanded form, a^2+b^2+c^2+2ab+2ca+2bc=81. Since ab + bc + ca = 26, we can multiply that by two to get 2ab + 2bc + 2ca = 52. Subtract that from our first equation, and we get a^2+b^2+c^2=81-52=29