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KCET2009MathematicsQuadratic Equation

If and are the roots of x²+x+1=0 , then ¹⁶+ ¹⁶ is equal to

Options

  1. A1
  2. B-1
  3. C2
  4. D0

Correct answer

B. -1

Step-by-step solution

Given, equation is x²+x+1=0 aligned & x = -1 3 i 2 & x = , ² & Since, and are the roots of x ²+ x +1=0 & aligned =& and = ² Now, ¹⁶+ ¹⁶ &=( )¹⁶+ ( ² )¹⁶ &= ¹⁶+ ³² &= + ² &=-1 ( ³=1 ) aligned aligned

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