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MHT CET20249 May 2024Morning ShiftMathematicsTrigonometric EquationsActual

The general solution of x-3 2 x+ 3 x= x-3 2 x+ 3 x is

Options

  1. Ax= n + 4 , n Z
  2. Bx=2 n + 4 , n Z
  3. Cx= n +(-1)^ n 4 , n Z
  4. Dx= n 2 + 8 , n Z

Correct answer

D. x= n 2 + 8 , n Z

Step-by-step solution

aligned & x-3 2 x+ 3 x & = x-3 2 x+ 3 x & ( x+ 3 x)-3 2 x-( x+ 3 x) & +3 2 x=0 & 2 2 x x-3 2 x-2 2 x x & +3 2 x=0 & 2 x(2 x-3)- 2 x(2 x-3)=0 & ( 2 x- 2 x)(2 x-3)=0 & 2 x= 2 x [ x 3 2 ] aligned aligned & 2 x= ( 2 -2 x ) & 2 x=2 n ( 2 -2 x ) aligned Neglecting (-) sign, we get x= n 2 + 8

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