Verified Solution • 2025–26 Session moderate

QJEEM21Ma0b89: JEE Main 2021 Mathematics - Class 11 JEEM21Ma0b89 Solution: Let , be two roots of the equation x 2 + (20) 1/4 x + (5) 1/2 = …

Let α\alpha , β\beta be two roots of the

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

Multiple Choice Options

  • A 10
  • B 100
  • C 50
  • D 160

Step-by-Step Verified Solution

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

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

Squaring both sides, we get

(x2+5)2=20x2{\left( {{x^2} + \sqrt 5 } \right)^2} = \sqrt {20} {x^2}

⇒\Rightarrow x4 = −- 5 ⇒\Rightarrow x8 = 25

⇒\Rightarrow α\alpha 8 + β\beta 8 = 50

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