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Paragraph: In reducing a given equation to the standard forms ( x= etc ) we apply several trigonometric or algebraic transformations. As a result of which the canonical form finally obtained may not be equivalent to the original equation resulting either in loss of solutions or in the appearance of fake solutions Question: The solution set of the equation 5-2 x =6 x-1 is

Options

  1. An +(-1)^n ⁻¹ (- 2 9 ) or x = n +(-1)^n 6
  2. Bn +(-1)^n 6
  3. Cn +(-1)^n ⁻¹ ( 2 9 )
  4. DNull set

Correct answer

B. n +(-1)^n 6

Step-by-step solution

Let x = t ; t [-1,1] 5-2 t =6 t-1 0 i.e. t 1 6 So, t [ 1 6 , 1 ] Now squaring, 5-2 t =(6 t -1), t = 1 2 ,- 2 9 , t =- 2 9 not possible ( t [ 1 6 , 1 ] ) So, t= 1 2 , x= 1 2 = 6 , x=n +(-1)^n 6

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