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JEE Advanced2009MathematicsTrigonometric EquationsActual

If ^4 x 2 + ^4 x 3 = 1 5 , then

Options

  1. A^2 x= 2 3
  2. B^8 x 8 + ^8 x 27 = 1 125
  3. C^2 x= 1 3
  4. D^8 x 8 + ^8 x 27 = 2 125

Correct answer

A. ^2 x= 2 3

Step-by-step solution

aligned & ^4 x 2 + ^4 x 3 = 1 5 & ^4 x 2 + (1- ^2 x )^2 3 = 1 5 & ^4 x 2 + 1+ ^4 x-2 ^2 x 3 = 1 5 & 5 ^4 x-4 ^2 x+2= 6 5 & 25 ^4 x-20 ^2 x+4=0 & (5 ^2 x-2 )^2=0 & ^2 x= 2 5 , ^2 x= 3 5 , ^2 x= 2 3 & ^8 x 8 + ^8 x 27 = 1 125 & aligned

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