Question

设{a_n}为公比q＞1的等比数列，若a₂₀₀₉和a₂₀₁₀是方程4x²-8x+3=0的两根，则a₂₀₁₁+a₂₀₁₂=

1. A.
   18
2. B.
   10
3. C.
   25
4. D.
   9

Answer 1

A
分析：根据{a_n}为公比q＞1的等比数列，若a₂₀₀₉和a₂₀₁₀是方程4x²-8x+3=0的两根，可得a₂₀₀₉=，a₂₀₁₀=，从而可确定公比q，进而可得a₂₀₁₁+a₂₀₁₂的值．
解答：∵{a_n}为公比q＞1的等比数列，若a₂₀₀₉和a₂₀₁₀是方程4x²-8x+3=0的两根
∴a₂₀₀₉=，a₂₀₁₀=
∴q=3
∴a₂₀₁₁+a₂₀₁₂=
故选A．
点评：本题考查根与系数的关系，考查等比数列，确定方程的根是关键．