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MHT CET202314 May 2023Morning ShiftMathematicsTrigonometric EquationsActual

The principal solutions of the equation x+ x=2 x are

Options

  1. A6 , 5 6
  2. B6 , 20
  3. C6 , 2 3
  4. D6 , 12

Correct answer

A. 6 , 5 6

Step-by-step solution

The given equation is defined for x 2 , 3 2 . Now, x+ x=2 x aligned & x x + 1 x =2 x & ( x+1)=2 ^2 x & ( x+1)=2 (1- ^2 x ) & ( x+1)=2(1- x)(1+ x) & (1+ x)[2(1- x)-1]=0 & 2(1- x)-1=0 & [ array r x -1 otherwise x=0 and x, x will be undefined array ] & x= 1 2 & x= 6 , 5 6 in (0,2 ) aligned

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