作业帮已知｛an｝为等比数列,a4＋a7＝2,a5＊a6＝－8,则a1＋a10＝?
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已知｛an｝为等比数列,a4＋a7＝2,a5＊a6＝－8,则a1＋a10＝?
已知｛an｝为等比数列,a4＋a7＝2,a5＊a6＝－8,则a1＋a10＝?
已知｛an｝为等比数列,a4＋a7＝2,a5＊a6＝－8,则a1＋a10＝?
由于是等比数列,a4*a7=a5*a6=-8
a4+a7=2
解方程有(a4-a7)^2=(a4+a7)^2-4a4*a7=4-4*(-8)=36
所以a4=4,a7=-2或a4=-2 a7=4
a1:a4=a4:a7
所以a1=a4^2/a7,同理,a10=a7^2/a4
a4=4,a7=-2时,a1＋a10＝-7
a7=4,a4=-2时,a1＋a10＝-7
31.75
a5＊a6=a4＊a7
算出q
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a4＋a7＝2 a1*q^3+a1q^6=2
a5＊a6=-8 a1²q^9=-8 a1q^3 * a1q^6=-8
令x1= a1q^3 x2= a1q^6
则X1*X2=-8 ,X1+X2=2
则X1，X2是方程x²-2x-8=0的两个实数根
解得：x1=4，X2=-2
先计算 a1q^3=4 则 a1q...
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a4＋a7＝2 a1*q^3+a1q^6=2
a5＊a6=-8 a1²q^9=-8 a1q^3 * a1q^6=-8
令x1= a1q^3 x2= a1q^6
则X1*X2=-8 ,X1+X2=2
则X1，X2是方程x²-2x-8=0的两个实数根
解得：x1=4，X2=-2
先计算 a1q^3=4 则 a1q^6=-2
则q^3=-1/2 q^6=1/4
a1=-8
a1＋a10＝a1+a1*q^3q^6=-8+(-8)(-1/8)=-7
如a1q^3=-2 则 a1q^6=4
则q^3=-2 q^6=4
a1=1
a1＋a10＝a1+a1*q^3q^6=1+(-2*4)=-7
收起
因为等比数列a5*a6 = a4*a7
(a4+a7)²=a4² + 2*(-8) + a7² = 4 所以 a4² + a7² = 20
( a4² + a7²)/a4a7 = (1/q^3 + q^3) = 20/(-8)= -5/2
(a4+a7)* (1/q^3 + q^3) = (a1 + a7 + a4 + a10) = a1+a10 + 2
所以a1+a10 = 2*(-5/2) -2 = -5-2 = -7