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Manipal MET2010MathematicsTrigonometric Equations

The sum of all the solutions of the equation x ( 3 +x ) ( 3 -x )= 1 4 , x [0,6 ] is

Options

  1. A15
  2. B30
  3. C110 3
  4. DNone of these

Correct answer

B. 30

Step-by-step solution

We have, x ( 3 +x ) ( 3 -x )= 1 4 x ( 1 4 ^2 x- 3 4 ^2 x )= 1 4 or, x 4 (4 ^2 x-3 )= 1 4 4 ^3 x-3 x=1 ( 3 x=4 ^3 x-3 x ) or, 3 x=1 3 x=2 n x= 2 n 3 , where n=0,1,2,3,4,5,6,7,8,9( x [0,6 ]) The required sum = 2 3 _ n=0 ^9 n=30

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