Let [], [] be two roots of the equation x2 + (20)1/4x + (5)1/2 = 0.

Question

Let $$\alpha$$, $$\beta$$ be two roots of the

equation x2 + (20)1/4x + (5)1/2 = 0. Then $$\alpha$$8 + $$\beta$$8 is equal to

Accepted Answer

x2 + (20)1/4x + (5)1/2 = 0

$$ \Rightarrow $$ x2 + $$\sqrt 5$$ = - (20)1/4x

Squaring both sides, we get

$${\left( {{x^2} + \sqrt 5 } \right)^2} = \sqrt {20} {x^2}$$

$$ \Rightarrow $$ x4 = -5 $$\Rightarrow$$ x8 = 25

$$ \Rightarrow $$ $$\alpha$$8 + $$\beta$$8 = 50

Solutions · 1