+306 Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.
+129845 Simplify as
x^2 + 12x - 4 = 0
We have the form ax^2 + bx + c = 0
Call the roots m , n
Product of the roots = c / a = -4/1 = -4
mn =-4
2mn = -8
Sum of the roots m + n = -b/a
m + n = - 12/ 1 = -12
(m + n)^2 = (-12)^2
m^2 + 2mn + n^2 = 144
m^2 - 8 + n^2 =144
m^2 + n^2 = 144 + 8 = 152
