+1418 Let a and b be the roots of the quadratic $x^2 - 5x + 3 = 4x^2 - 8x + 23$ Find the quadratic whose roots are a^4 and b^4.
+129771 Simplify as
3x^2 -3x + 20 = 0
Product of roots = ab = 20/3
2ab = 40/3
Sum of roots = a + b = - (-3) / 3 = 1
Square both sides
a^2 + 2ab + b^2 = 1
a^2 + b^2 + 40/3 = 1
a^2 + b^2 = -37/3 square both sides
a^4 + 2(ab)^2 + b^4 = 1369 / 9
a^4 + b^4 + 2(20/3)^2 = 1369 / 9
a^4 + b^4 + 800/9 = 1369/9
a^4 + b^4 = 569 / 9
