等比数列的前三项和为168,a2*a5=42,求a6

设等比数列的第一项为a1,公比为q，那末a2=a1*q,a3=a1*q*q,a4=a1*q*q*q,a5=a1*q*q*q*q,
将上述结果带入a1+a2+a3=168和a2*a5=42,组成方程组，就这个方程组就可以得到原始数据a1和q,这样a6也就轻松得到了。

>> [a,q]=solve('a*(1+q+q^2)-168=0','a^2*q^5-42=0','a,q')
a =
119.20689035758144068333445851826
156.36366254051205597017003904258-47.469747489656238958112044329905*i
204.03289228069722368816273169830-20.317000840188657242033100304375*i
204.03289228069722368816273169830+20.317000840188657242033100304375*i
156.36366254051205597017003904258+47.469747489656238958112044329905*i
q =
.31198183952016233717742279931626
.53626889262154021237010436362974e-1+.26972390191281752291610673377378*i
-.20887376140318757077810278840206+.13943509098092458998395590708750*i
-.20887376140318757077810278840206-.13943509098092458998395590708750*i
.53626889262154021237010436362974e-1-.26972390191281752291610673377378*i
>> q1=q(1);a1=a(1);
>> a6=a1*q1^5
a6 =
.35232862692763666587757313118912
>>
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