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AP EAMCET202018 Sep 2020Evening ShiftMathematicsTrigonometric EquationsActual

Find the general solution of ' ( x+ 2 x ) (+ 3 x= x+ 2 x+ 3 x^ )

Options

  1. A(2 n + 2 3 , n 2 + 8 , n Z )
  2. B(2 n - 2 3 , n 2 - 8 , n Z )
  3. C(2 n + 2 3 , n 2 8 , n Z )
  4. D(2 n 2 3 , n 2 + 8 , n Z )

Correct answer

D. (2 n 2 3 , n 2 + 8 , n Z )

Step-by-step solution

( aligned & x+ 2 x+ 3 x= x+ 2 x+ 3 x & ( x+ 3 x)+ 2 x=( x+ 3 x)+ 2 x & 2 ( 4 x 2 ) ( 2 x 2 )+ 2 x=2 ( 4 x 2 ) ( 2 x 2 )+ 2 x & 2 2 x x+ 2 x=2 2 x x+ 2 x & 2 x(2 x+1)= 2 x(2 x+1) & ( 2 x- 2 x)(2 x+1)=0 & 2 x- 2 x=0 (or) 2 x+1=0 & 2 x=1= 4 & 2 x=n + 4 x= n 2 + 8 & or x= -1 2 & x= 2 3 & x=2 n 2 3 aligned ) Hence, option (d) is correct.

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