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AP EAMCET202315 May 2023Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If x= 5 4 , then 3 x=

Options

  1. A63 65
  2. B25 26
  3. C65 67
  4. D252 265

Correct answer

A. 63 65

Step-by-step solution

Given, x= 5 4 e^x+e^ -x = 5 2 Now, (e^x+e^ -x )^3=e^ 3 x +e^ -3 x +3 e^x e^ -x (e^x+e^ -x ) 125 8 =e^ 3 x +e^ -3 x + 15 2 e^ 3 x +e^ -3 x = 65 8 and ^2 x- ^2 x=1 x= 3 4 aligned & e^x-e^ -x = 3 2 & (e^x-e^ -x )^3=e^ 3 x -e^ -3 x -3 e^x e^ -x (e^x-e^ -x ) & 27 8 =e^ 3 x -e^ -3 x -3 5 2 e^ 3 x -e^ -3 x = 63 8 aligned Now, 3 x= 3 x 3 x = 63 8 8 65 = 63 65

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