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BITSAT2009MathematicsBinomial TheoremActual

The general solution of (8 ^2 x 2 =1+ x ) is

Options

  1. A(2 n ⁻¹ ( -1 3 ) )
  2. B(2 n 6 )
  3. C(2 n ⁻¹ ( 1 3 ) )
  4. DNone of these

Correct answer

C. (2 n ⁻¹ ( 1 3 ) )

Step-by-step solution

We have, (8 ^2 x 2 =1+ x ) ( aligned & 8 ( 1- x 1+ x )=1+ 1 x = 1+ x x & 8 x-8 ^2 x=(1+ x)^2 & 9 ^2 x -6 x +1=0 & (3 x -1)^2=0 3 x -1=0 & x = 1 3 = (say) x =2 n & x =2 n ⁻¹ ( 1 3 ) where n I aligned )

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