等比数列

更新时间2021-04-22 19:57:49

a1+a1q=4      a1q²+a1=8   我要求a1和q怎么求 要万能一点的方法

a1 + a1q = 4，a1 = 4/( 1 + q )；

a1q^2 + a1 = 8，a1 = 8/( 1 + q^2 )

故 4/( 1 + q ) = 8/( 1 + q^2 )

q^2 - 2q + 1 = 2

( q - 1 )^2 = 2

q = 1 ± √2；

q = 1 + √2，a1 = 4/( 2 + √2 ) = 4( 2 - √2 )/[ ( 2 + √2 )( 2 - √2 ) ] = 4 - 2√2 ；

q = 1 - √2，a1 = 4/( 2 - √2 ) = 4( 2 + √2 )/[ ( 2 + √2 )( 2 - √2 ) ] = 4 + 2√2 。