Let α, β be two roots of the equation x2+(20)1 / 4 x+(5)1 / 2=0. Then α8+β8 is equal to

Question

Let α, β be two roots of the equation x2+(20)1 / 4 x+(5)1 / 2=0. Then α8+β8 is equal to (A) 10 (B) 100 (C) 50 (D) 160

Tardigrade Admin · Accepted Answer

(x2+√5)2=√20 x2 x4=-5 ⇒ x8=25 α8+β8=50

Q. Let $α, β$ be two roots of the equation $x^{2} + (20)^{1/4} x + (5)^{1/2} = 0$ . Then $α^{8} + β^{8}$ is equal to