Maths · Relations between roots and coefficients, nature of roots

If then is equal to

If \( x+\frac{1}{x}=4, \) then \( x^{4}+\frac{1}{x^{4}} \) is equal to

  • A. 196
  • B. 194
  • C. 192 \)
  • D. 19

Step-by-step solution

Given x + 1/x = 4. Squaring gives x^2 + 1/x^2 + 2 = 16, so x^2 + 1/x^2 = 14. Squaring again: (x^2 + 1/x^2)^2 = x^4 + 1/x^4 + 2 = 196, hence x^4 + 1/x^4 = 194.
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