Let a and b be the roots of x^2 - 3x + 1 = 0. Find a^2 + b^2.
The sum of the roots = 3
So
a + b = 3 square both sides
a^2 + 2ab + b^2 = 9 (1)
The product of the roots = 1
So ab = 1 (2)
Sub (2) into (1)
a^2 + 2(1) + b^2 = 9
a^2 + 2 + b^2 = 9
a^2 + b^2 = 7
