<prompt> Acha fx iwe polynomial yenye coefficients halisi, zisizo hasi. Ikiwa f6 24 na f24 1536, pata thamani kubwa zaidi ya f12.  <response>: Hebufx a_n xn a_n - 1 xn - 1 vitone a_1 x a_0.Kisha kutoka kwa maelezo uliyopewa,anzaaligna_n cdoti 6n a_n - 1 cdoti 6n - 1 vitone a_1 cdoti 6 a_0 24, a_n cdoti 24n a_n - 1 cdoti 24n - 1 vitone a_1 cdoti 24 a_0 1536.endalignKisha kwa Cauchy-Schwarz,anzaaligna_n cdoti 6n a_n - 1 cdoti 6n - 1 vitone a_1 cdoti 6 a_0a_n cdot 24n a_n - 1 cdoti 24n - 1 vitone a_1 cdoti 24 a_0 ge a_n cdot 12n a_n - 1 cdoti 12n - 1 vitone a_1 cdot 12 a_02.endalignKwa maneno mengine, f122 le 24 cdot 1536 36864, hivyo f12 le 192.Usawa hutokea kwa fx fracx39, kwa hivyo thamani ya juu ni 192. 