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AP EAMCET202315 May 2023Morning ShiftMathematicsQuadratic EquationActual

If (3+2 2 )^ x^2-4 +(3-2 2 )^ x^2-4 =6 , then x^4+x^2+5=

Options

  1. A-30
  2. B-35
  3. C30
  4. D35

Correct answer

D. 35

Step-by-step solution

Since (3+2 2 ) (3-2 2 )=9-8=1 (3-2 2 )= 1 (3+2 2 ) Now (3+2 2 )^ x^2-4 +(3-2 2 )^ x^2-4 =6 (3+2 2 )^ x^2-4 + 1 (3+2 2 )^ x^2-4 =6 Let y=(3+2 2 )^ x^2-4 y+ 1 y =6 y^2-6 y+1=0 y=3+2 2 or y=3-2 2 (3+2 2 )^ x^2-4 =(3+2 2 ) or (3+2 2 )^ x^2-4 = 1 (3+2 2 ) x^2-4=1 or x^2-4=-1 x= 5 or x=3 i Since x=3 i is imaginary Hence x= 5 Therefore x^4+x^2+5=35

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