Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.
Simplify as
x^2 + 10x - 4 = 0
Call the roots a,b
Product of roots = ab = -4
Sum of roots = a + b = -10 square both sides
a^2 + 2ab + b^2 = 100
a^2 + 2(-4) + b^2 =100
a^2 + b^2 - 8 = 100
a^2 + b^2 = 108
