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Category: Algebra

solve-inside-N-2-x-x-1-4y-y-1-

Question Number 73033 by mathmax by abdo last updated on 05/Nov/19 $${solve}\:{inside}\:{N}^{\mathrm{2}} \:\:\:\:{x}\left({x}+\mathrm{1}\right)=\mathrm{4}{y}\left({y}+\mathrm{1}\right) \\ $$ Answered by mind is power last updated on 05/Nov/19 $$\Leftrightarrow\mathrm{4x}\left(\mathrm{x}+\mathrm{1}\right)=\mathrm{16y}\left(\mathrm{y}+\mathrm{1}\right)…

x-and-y-are-reals-or-complex-let-put-x-0-1-x-1-x-x-2-x-x-1-x-n-x-x-1-x-2-x-n-1-prove-that-x-y-n-k-0-n-C-n-k-x-n-k-y-k-

Question Number 73027 by mathmax by abdo last updated on 05/Nov/19 $${x}\:{and}\:{y}\:{are}\:{reals}\left({or}\:{complex}\right)\:{let}\:{put}\:{x}^{\left(\mathrm{0}\right)} =\mathrm{1}\:,{x}^{\left(\mathrm{1}\right)} ={x} \\ $$$${x}^{\left(\mathrm{2}\right)} ={x}\left({x}−\mathrm{1}\right)…..{x}^{\left({n}\right)} ={x}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)…\left({x}−{n}+\mathrm{1}\right){prove}\:{that} \\ $$$$\left({x}+{y}\right)^{\left({n}\right)} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:\:{x}^{\left({n}−{k}\right)}…