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Question Number 93626 by i jagooll last updated on 14/May/20

Commented by MJS last updated on 14/May/20

$$\mathrm{with}\mathrm{any}\mathrm{number}\in \mathbb{C}\mathrm{you}\mathrm{like}$$

Commented by john santu last updated on 14/May/20

$$\mathrm{real}\mathrm{number}\mathrm{sir}$$

Commented by i jagooll last updated on 14/May/20

$$\mathrm{yes}\mathrm{sir}.\mathrm{if}\mathrm{real}\mathrm{number}\mathrm{or}\mathrm{complex}$$$$\mathrm{number}.\mathrm{how}\mathrm{to}\mathrm{solve}\mathrm{sir}?$$

Commented by MJS last updated on 14/May/20

$$x\in \mathbb{C}\mathrm{is}\mathrm{possible}\Rightarrow x\in \mathbb{R}\mathrm{is}\mathrm{also}\mathrm{possible}$$$$$$$$\mathrm{what}\mathrm{are}\mathrm{we}\mathrm{allowed}\mathrm{to}\mathrm{do}?$$$${\mathrm{there}}^{\prime }\mathrm{s}\mathrm{a}\mathrm{unique}\mathrm{polynome}\mathrm{of}{6}^{\mathrm{th}}\mathrm{degree}$$$$f\left(x\right)=\underset{j=0}{\sum ^6}{c}_j{x}^j\mathrm{with}f\left(1\right)=9,f\left(2\right)=18,...f\left(7\right)=104$$$$\mathrm{but}\mathrm{if}\mathrm{we}\mathrm{are}\mathrm{free}\mathrm{to}\mathrm{use}\mathrm{any}\mathrm{model},\mathrm{why}\mathrm{not}$$$$\mathrm{use}g\left(x\right)=\underset{j=0}{\sum ^6}\frac{c_j}{x^j}?\mathrm{this}\mathrm{also}\mathrm{leads}\mathrm{to}\mathrm{an}\mathrm{unique}$$$$\mathrm{solution}.\mathrm{or}\mathrm{use}\mathrm{any}\mathrm{of}\mathrm{the}\mathrm{zillions}\mathrm{of}\mathrm{possibilities}$$$$$$$$\mathrm{or}\mathrm{just}\mathrm{insert}\mathrm{your}\mathrm{birth}\mathrm{date}.\mathrm{we}\mathrm{can}\mathrm{find}\mathrm{a}$$$$\mathrm{function}h\left(x\right)\mathrm{with}h\left(8\right)=\frac{{\pi }^{\mathrm{e}}}{\gamma }...$$

Commented by prakash jain last updated on 14/May/20

$$\mathrm{Given}\mathrm{any}\mathrm{finite}\mathrm{sequence}\mathrm{there}$$$$\mathrm{infinite}\mathrm{number}\mathrm{of}\mathrm{formulas}\mathrm{for}{a}_n$$$$\mathrm{which}\mathrm{sstify}\mathrm{the}\mathrm{finite}\mathrm{terms}.$$

Commented by i jagooll last updated on 14/May/20

hahaha...����

Commented by prakash jain last updated on 14/May/20

$$\mathrm{Let}\mathrm{me}\mathrm{explain}\mathrm{given}$$$$a_1,a_2,a_3$$$$$$$$a_n=\frac{a_1(n-2)(n-3)}{(-1)(-2)}+\frac{a_2(n-1)(n-3)}{\left(1\right)(-1)}$$$$+\frac{a_3(n-1)(n-2)}{\left(2\right)\left(1\right)}$$$$+b_n(n-1)(n-2)(n-3)$$$$\mathrm{This}\mathrm{will}\mathrm{given}\mathrm{condition}\mathrm{for}\mathrm{given}\mathrm{finite}\mathrm{set}$$$$\mathrm{numbers}\mathrm{for}\mathrm{any}{b}_n.$$$$\mathrm{You}\mathrm{can}\mathrm{extend}\mathrm{this}\mathrm{for}\mathrm{more}\mathrm{three}$$$$\mathrm{givdn}\mathrm{numbers}.$$

Commented by prakash jain last updated on 14/May/20

I hope you get general idea about why answers are not unique.

Commented by i jagooll last updated on 14/May/20

thank you sir. i can try

Answered by MJS last updated on 14/May/20

$$\mathrm{if}{\mathrm{it}}^{\prime }\mathrm{s}\mathrm{a}\mathrm{polynome}\mathrm{calculate}\mathrm{the}\mathrm{differences}$$$$\mathrm{and}\mathrm{continue}\mathrm{until}\mathrm{all}\mathrm{numbers}\mathrm{in}\mathrm{a}\mathrm{line}\mathrm{are}$$$$\mathrm{equal}.\mathrm{then}\mathrm{go}\mathrm{back}$$$$91820616379104-558$$$$924121625-662$$$$-739-39149-687$$$$46-7853-5-696$$$$-124131-58-691$$$$255-189-633$$$$-444$$

Commented by i jagooll last updated on 14/May/20

$$\mathrm{thanks}\mathrm{sir}.$$

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