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Question-211636




Question Number 211636 by BaliramKumar last updated on 15/Sep/24
Answered by Rasheed.Sindhi last updated on 15/Sep/24
▶A=x^(8k+3) +x^(8k+6) +x^(8k+9) +x^(8k+12)           =x^(8k+3) (1+x^3 +x^6 +x^9 )  ▶B=(1+x^3 )(1+x^6 )           =1+x^3 +x^6 +x^9   (A/B)=x^(8k+3)
$$\blacktriangleright{A}={x}^{\mathrm{8}{k}+\mathrm{3}} +{x}^{\mathrm{8}{k}+\mathrm{6}} +{x}^{\mathrm{8}{k}+\mathrm{9}} +{x}^{\mathrm{8}{k}+\mathrm{12}} \\ $$$$\:\:\:\:\:\:\:\:={x}^{\mathrm{8}{k}+\mathrm{3}} \left(\mathrm{1}+{x}^{\mathrm{3}} +{x}^{\mathrm{6}} +{x}^{\mathrm{9}} \right) \\ $$$$\blacktriangleright{B}=\left(\mathrm{1}+{x}^{\mathrm{3}} \right)\left(\mathrm{1}+{x}^{\mathrm{6}} \right) \\ $$$$\:\:\:\:\:\:\:\:\:=\mathrm{1}+{x}^{\mathrm{3}} +{x}^{\mathrm{6}} +{x}^{\mathrm{9}} \\ $$$$\frac{{A}}{{B}}={x}^{\mathrm{8}{k}+\mathrm{3}} \\ $$
Commented by BaliramKumar last updated on 15/Sep/24
thanks
$${thanks} \\ $$

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