If a and b are the solutions of x^2 - 2x + 6 = 0, what is the value of a^4 + b^4?
+128475 By Vieta, the product of the roots =
6/1 = ab = 6 (1)
And the sum of the roots =
2/1 = 2 = a + b
a + b = 2 square both sides
a^2 + 2ab + b^2 = 4 sub (1) into this
a^2 + 2(6) + b^2 = 4
a^2 + b^2 = -8
Square both sides again
a^4 + 2(a^2b^2) + b^4 = 64
a^4 + 2(ab)^2 + b^4 = 64 sub (1) in
a^4 + 2(6)^2 + b^4 = 64
a^4 + b^4 + 72 = 64
a^4 + b^4 = -8
