Let $\alpha$, $\beta$ be two roots of the
equation x2 + (20)1/4x + (5)1/2 = 0. Then $\alpha$8 + $\beta$8 is equal to
Solution
x<sup>2</sup> + (20)<sup>1/4</sup>x + (5)<sup>1/2</sup> = 0
<br/><br/>$\Rightarrow$ x<sup>2</sup> + $\sqrt 5$ = - (20)<sup>1/4</sup>x
<br/><br/>Squaring both sides, we get
<br/><br/>${\left( {{x^2} + \sqrt 5 } \right)^2} = \sqrt {20} {x^2}$<br><br>$\Rightarrow$ x<sup>4</sup> = $-$5 $\Rightarrow$ x<sup>8</sup> = 25<br><br>$\Rightarrow$ $\alpha$<sup>8</sup> + $\beta$<sup>8</sup> = 50
About this question
Subject: Mathematics · Chapter: Complex Numbers and Quadratic Equations · Topic: Complex Numbers and Argand Plane
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