Question-148861

Question Number 148861 by mathdanisur last updated on 31/Jul/21

Answered by dumitrel last updated on 01/Aug/21

(2x)^4 +324=(4x^2 −12x+18)(4x^2 +12x+18) f(x)=4x^2 −12x+18⇒f(x+3)=4x^2 +12x+18 (2x)^4 +324=f(x)∙f(x+3) ((f(5)f(8)f(11)f(14)f(17)f(20)f(23)f(26)f(29)f(32))/(f(2)f(5)f(8)f(11)f(14)f(17)f(20)f(23)f(26)f(29)))=((f(32))/(f(2)))=373

$$\left(\mathrm{2}{x}\right)^{\mathrm{4}} +\mathrm{324}=\left(\mathrm{4}{x}^{\mathrm{2}} −\mathrm{12}{x}+\mathrm{18}\right)\left(\mathrm{4}{x}^{\mathrm{2}} +\mathrm{12}{x}+\mathrm{18}\right) \\ $$$${f}\left({x}\right)=\mathrm{4}{x}^{\mathrm{2}} −\mathrm{12}{x}+\mathrm{18}\Rightarrow{f}\left({x}+\mathrm{3}\right)=\mathrm{4}{x}^{\mathrm{2}} +\mathrm{12}{x}+\mathrm{18} \\ $$$$\left(\mathrm{2}{x}\right)^{\mathrm{4}} +\mathrm{324}={f}\left({x}\right)\centerdot{f}\left({x}+\mathrm{3}\right) \\ $$$$\frac{{f}\left(\mathrm{5}\right){f}\left(\mathrm{8}\right){f}\left(\mathrm{11}\right){f}\left(\mathrm{14}\right){f}\left(\mathrm{17}\right){f}\left(\mathrm{20}\right){f}\left(\mathrm{23}\right){f}\left(\mathrm{26}\right){f}\left(\mathrm{29}\right){f}\left(\mathrm{32}\right)}{{f}\left(\mathrm{2}\right){f}\left(\mathrm{5}\right){f}\left(\mathrm{8}\right){f}\left(\mathrm{11}\right){f}\left(\mathrm{14}\right){f}\left(\mathrm{17}\right){f}\left(\mathrm{20}\right){f}\left(\mathrm{23}\right){f}\left(\mathrm{26}\right){f}\left(\mathrm{29}\right)}=\frac{{f}\left(\mathrm{32}\right)}{{f}\left(\mathrm{2}\right)}=\mathrm{373} \\ $$$$ \\ $$$$ \\ $$

Commented by mathdanisur last updated on 01/Aug/21