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Question Number 20881 by tawa tawa last updated on 05/Sep/17

Answered by mrW1 last updated on 06/Sep/17

$${(\mathrm{ax}+\mathrm{ay})}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{n}}{(\mathrm{x}+\mathrm{y})}^{\mathrm{n}}$$$$\mathrm{since}\mathrm{a}\mathrm{middle}\mathrm{term}\mathrm{exists},\mathrm{n}\mathrm{is}\mathrm{even}.$$$$\mathrm{its}\mathrm{middle}\mathrm{term}\mathrm{is}$$$${\mathrm{a}}^{\mathrm{n}}{\mathrm{C}}_{\frac{\mathrm{n}}{2}}^{\mathrm{n}}{\mathrm{x}}^{\frac{\mathrm{n}}{2}}{\mathrm{y}}^{\frac{\mathrm{n}}{2}}={14580\mathrm{x}}^3{\mathrm{y}}^3$$$$\Rightarrow \frac{\mathrm{n}}{2}=3\Rightarrow \mathrm{n}=6$$$${\mathrm{C}}_3^6=20$$$${\mathrm{a}}^6\times 20=14580$$$$\Rightarrow \mathrm{a}={\left(\frac{14580}{20}\right)}^{\frac{1}{6}}=3$$

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

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$$$$$

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