Multiple choice

If α and β are the roots of the equation 5𝑥2 ﹣4𝑥 + 1 = 0, then find the value of α + β + α3 + β3 + α5 + β5 + ⋯∞.

  1. 0.5

  2. 0.8

  3. 1.2

  4. 1
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B Correct answer
Explanation

The sum is an infinite geometric series: (alpha + beta) + (alpha^3 + beta^3) + ... This is not a simple geometric series. However, evaluating the sum of roots alpha + beta = 4/5 = 0.8 and product alpha * beta = 1/5 = 0.2. The series is (alpha + beta) + (alpha^3 + beta^3) + ... which converges to 0.8.

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