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COMEDK2022MathematicsTrigonometric Equations

Find the general solution of 2 x+ x=0 .

Options

  1. A(n 1) 2
  2. Bn 2
  3. Cn +(-1)^n 7 6 or (2 n 1) 2
  4. DNone of the above

Correct answer

C. n +(-1)^n 7 6 or (2 n 1) 2

Step-by-step solution

The given equation is 2x + x = 0 . Using the double angle identity 2x = 2 x x , the equation becomes 2 x x + x = 0 . Factoring out x , we get x (2 x + 1) = 0 . This implies either x = 0 or 2 x + 1 = 0 . For x = 0 , the general solution is x = (2n + 1) 2 , which can also be written as n 2 . For 2 x + 1 = 0 , we have x = - 1 2 . Since x = - 6 = (- 6 ) = ( + 6 ) = ( 7 6 ) , the general solution is x = n + (-1)^n (- 6 ) or x = n + (-1)^n 7 6 . Comparing these results with the given options, the solution set is x = n +

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