设a1，a2，…a10成等比数列，且a1a2…a10=32，记x=a1+a2+…+a10，y=1a1+1a2+…+1a10，则xy=．

Question

设a₁，a₂，…a₁₀成等比数列，且a₁a₂…a₁₀=32，记x=a₁+a₂+…+a₁₀，y=(1)/(a1)+(1)/(a2)+…+(1)/(a10)，则(x)/(y)=______．

Answer 1

∵a₁，a₂，…a₁₀成等比数列，且a₁a₂…a₁₀=32，
∴a₁•a₁₀=a₂•a₉=a₃•a₈=a_4•a₇=a₅•a₆=2
∴y=(1)/(a1)+(1)/(a2)+…+(1)/(a10)
=(1)/(2)((2)/(a1)+(2)/(a2)+…+(2)/(a10))
=(1)/(2)((a1a10)/(a1)+(a2a9)/(a2)+…+(a10a1)/(a10))
=(1)/(2)（a₁+a₂+…+a₁₀）
=(1)/(2)x
∴(x)/(y)=2
故答案为：2