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KVPY2012MathematicsTrigonometric Equations

The sum of all x [0, ] which satisfy the equation x+ 1 2 x= ² (x+ 4 ) is -

Options

  1. A6
  2. B5 6
  3. C2

Correct answer

C. 2

Step-by-step solution

array l x+ 1 2 x= ² (x+ 4 ) x+ 1 2 x= 1 2 (1- ( 2 +2 x ) . x+ 1 2 x= 1 2 (1+ 2 x) 2 x+ x=1+ x x 2 x x-2 x+1- x=0 (1- x)-2 x(1- x)=0 (1- x)(1-2 x)=0 1- x=0 & 1-2 x=0 x=1 x= 1 2 x=0, x= 6 , 5 6 sum =0+ 6 + 5 6 = array

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