Let $r$ and $s$ be the roots of $2x^2 + 5x - 13 = x^2 - 4x + 7.$ Find $r^2 + s^2.$
Simplify as
x^2 + 9x - 20 = 0
r + s = -9/1 = -9 square both sides
r^2 + 2rs + s^2 = 81 (1)
rs = -20 / 1 = -20
2rs = -40
So......using (1)
r^2 + 2 (-40) + s^2 = 81
r^2 - 80 + s^2 = 81
r^2 + s^2 = 81 + 80
r^2 + s^2 = 161
+1678 
