Question Number 20881 by tawa tawa last updated on 05/Sep/17
Answered by mrW1 last updated on 06/Sep/17
$$\left(\mathrm{ax}+\mathrm{ay}\right)^{\mathrm{n}} =\mathrm{a}^{\mathrm{n}} \left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{n}} \\ $$$$\mathrm{since}\:\mathrm{a}\:\mathrm{middle}\:\mathrm{term}\:\mathrm{exists},\:\mathrm{n}\:\mathrm{is}\:\mathrm{even}. \\ $$$$\mathrm{its}\:\mathrm{middle}\:\mathrm{term}\:\mathrm{is} \\ $$$$\mathrm{a}^{\mathrm{n}} \mathrm{C}_{\frac{\mathrm{n}}{\mathrm{2}}} ^{\mathrm{n}} \mathrm{x}^{\frac{\mathrm{n}}{\mathrm{2}}} \mathrm{y}^{\frac{\mathrm{n}}{\mathrm{2}}} =\mathrm{14580x}^{\mathrm{3}} \mathrm{y}^{\mathrm{3}} \\ $$$$\Rightarrow\frac{\mathrm{n}}{\mathrm{2}}=\mathrm{3}\Rightarrow\mathrm{n}=\mathrm{6} \\ $$$$\mathrm{C}_{\mathrm{3}} ^{\mathrm{6}} =\mathrm{20} \\ $$$$\mathrm{a}^{\mathrm{6}} ×\mathrm{20}=\mathrm{14580} \\ $$$$\Rightarrow\mathrm{a}=\left(\frac{\mathrm{14580}}{\mathrm{20}}\right)^{\frac{\mathrm{1}}{\mathrm{6}}} =\mathrm{3} \\ $$
Commented by tawa tawa last updated on 08/Sep/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$
Answered by myintkhaing last updated on 07/Sep/17
Commented by tawa tawa last updated on 08/Sep/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$$$ \\ $$