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AP EAMCET202318 May 2023Evening ShiftMathematicsTrigonometric EquationsActual

If 3 ^4 x+2 ^4 x= 6 5 and x is an acute angle, then 2 x =

Options

  1. A2 6 5
  2. B2 6
  3. C3 2 5
  4. D2 3 5

Correct answer

B. 2 6

Step-by-step solution

aligned & 3 ^4 x+2 ^4 x= 6 5 & 3 ^4 x+2 (1- ^2 x )^2= 6 5 & 3 ^4 x+2 (1+ ^4 x-2 ^2 x )= 6 5 & 25 ^4 x-20 ^2 x+4=0 & ^2 x= 20 400-400 2 25 = 2 5 & ^2 x=1- 2 5 = 3 5 & 2 x=2 2 5 3 5 = 2 5 6 & & 2 x=2 3 5 -1= 1 5 & 2 x=2 6 aligned

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