Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.
Simplify as
x^2 + 12x - 4 = 0
Let the roots = a,b
Sum of the roots = a + b = -12
Product of the roots = -4 = ab → -8 = 2ab
a + b = -12 square both sides
a^2 + 2ab + b^2 = 144
a^2 - 8 + b^2 =144
a^2 + b^2 = 152
+1222 
