等比数列
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 。
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