若数列{an}是等比数列,若a4a5=8,a3a4=4,则a1a2
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若数列{an}是等比数列,若a4a5=8,a3a4=4,则a1a2
若数列{an}是等比数列,若a4a5=8,a3a4=4,则a1a2
若数列{an}是等比数列,若a4a5=8,a3a4=4,则a1a2
a4a5=a1q^3*a1q^4=a1^2q^7=8,
a3a4=a1q^2a1q^3=a1^2q^5=4,
上式/下式得:q^2=2.q=(+/-)2^(1/2)
上式*下式:a1^4q^12=32
a1^4=32/q^12
a1^2=4根号2/q^6
a1a2=a1*a1q=a1^2q=4根号2/q^6*q=4根号2/q^5=4根号2/[(+/-)2^(1/2)]^5=(+/-)根号2/2
A4A5/A3A4=A5/A3=8/4=2=K(K为公比)
A1A2=A3/2K*A4/2K=A3A4/4K^2=1/4
a4 * a5 = 8
=> a*r^3 * a*r^4 = 8
=> a^2 * r^7 = 8 --------(1)
a3 * a4 = 4
=> a*r^2 * a*r^3 = 4
=> a^2 * r^5 = 4 ----------(2)
(1) / (2):
=> r = 2^(1/2) ...
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a4 * a5 = 8
=> a*r^3 * a*r^4 = 8
=> a^2 * r^7 = 8 --------(1)
a3 * a4 = 4
=> a*r^2 * a*r^3 = 4
=> a^2 * r^5 = 4 ----------(2)
(1) / (2):
=> r = 2^(1/2) ----------(3)
(3)代入(2)
a^2 * 2^[(1/2)*5] = 4
=> a^2 = 2^(-1/2) -------(4)
a1*a2
= a*a*r
= a^2 * r
= 2^(-1/2) * 2^(1/2)
= 1
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