Let \(a, b\) be distinct positive real numbers, whose geometric mean equals \(\frac{a^{t-99}+b^{t-99}}{a^{t-100}+b^{t-100}}\). Then \(t\) must equal

• Correct answer
  A

  \(\frac{199}{2}\)
• B

  \(\frac{99}{2}\)
• C

  199
• D

  99

Hence, the correct answer is option: 'A'.