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AP EAMCET202124 Aug 2021Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

The equation ^4 x+ ^4 x=a has real solutions, then

Options

  1. A1 < a < 5 2
  2. B1 2 a 1
  3. Ca 1 2
  4. D0 < a < 1

Correct answer

B. 1 2 a 1

Step-by-step solution

aligned & ^4 x+ ^4 x= has real solution. & Since, aligned & = ^4 x+ ^4 x &= ( ^2 x+ ^2 x )^2-2 ^2 x ^2 x &=(1)^2- 4 2 ^2 x ^2 x=1- (2 x x)^2 2 &=1- ( ^2 2 x ) 2 [ 2 A=2 A A] & -1 2 x 1 & 0 ^2 2 x 1 aligned aligned aligned 0 & ^2 2 x 2 1 2 - 1 2 & - ^2 2 x 2 0 1- 1 2 & 1- ^2 2 x 2 1 1 2 & 1 aligned

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