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COMEDK2013MathematicsQuadratic Equation

If x+ 1 x =2 , then x^ n + 1 x^ n is equal to

Options

  1. A2^ n
  2. B2^ n n
  3. C2 i n
  4. D2 n

Correct answer

D. 2 n

Step-by-step solution

We have, x+ 1 x =2 x²+1=2 x x²-(2 ) x+1=0 x= 2 4 ² -4 2 = 2 -4 ² 2 = 2 2( ) i 2 = ( ) i Now, x^ n =( ( ) i)^ n = n i n and 1 x^ n =( ( ) i)^ -n = n i n x^ n + 1 x^ n =( n i n )+( n i n )=2 n

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