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

Question

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, 10, 100, 50, 160

MARKS App · Accepted Answer

Given, x 2 + 20 1 / 4 x + 5 1 / 2 = 0 ⇒ x 2 + 5 = - x 20 1 4 ⇒ x 2 + 5 2 = 20 x 2 ⇒ x 4 + 5 + 2 × x 2 × 5 = 20 x 2 ⇒ x 4 = - 5 ⇒ x 8 = 25 So, α 8 + β 8 = 25 + 25 = 50

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