Question Number 73032 by mathmax by abdo last updated on 05/Nov/19 $${find}\:{x}\:{from}\:{n}\:\:/\:\exists{n}\in{N}^{{n}} \:\:\:\:{and}\:\mathrm{1}+{x}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{3}} \:+{x}^{\mathrm{4}} ={n}^{\mathrm{2}} \\ $$ Answered by mind is power last updated…
Question Number 73035 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:\:\forall{n}\in{N}^{\bigstar} \:\:\:\:\:\mathrm{2}!\mathrm{4}!….\left(\mathrm{2}{n}\right)!\geqslant\left\{\left({n}+\mathrm{1}\right)!\right\}^{{n}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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 $$\Leftrightarrow\mathrm{4x}\left(\mathrm{x}+\mathrm{1}\right)=\mathrm{16y}\left(\mathrm{y}+\mathrm{1}\right)…
Question Number 73031 by mathmax by abdo last updated on 05/Nov/19 $${solve}\:{inside}\:{N}^{\mathrm{2}} \:\:\:\mathrm{3}{x}^{\mathrm{3}} \:+{xy}\:+\mathrm{4}{y}^{\mathrm{3}} \:=\mathrm{349} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 138564 by DomaPeti last updated on 14/Apr/21 $${y}\centerdot{y}'=\mathrm{0}.\mathrm{5}\centerdot\left(\mathrm{1}+{y}\centerdot{c}_{\mathrm{1}} \right)^{\mathrm{2}} \centerdot{c}_{\mathrm{2}} +\mathrm{0}.\mathrm{5} \\ $$$$ \\ $$$${y}=? \\ $$ Answered by mr W last updated…
Question Number 73029 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:\:\forall\left({n},{p},{q}\right)\in{N}^{\mathrm{3}} \:\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{p}} ^{{k}} \:{C}_{{q}} ^{{n}−{k}} \:\:\:={C}_{{p}+{q}} ^{{n}} \\ $$$${conclude}\:{that}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\left({C}_{{n}} ^{{k}}…
Question Number 73028 by mathmax by abdo last updated on 05/Nov/19 $${calculate}\:\sum_{\mathrm{1}\leqslant{i}\leqslant{n}\:{and}\:\mathrm{1}\leqslant{j}\leqslant{n}} \:\:{min}\left({i},{j}\right) \\ $$ Answered by mind is power last updated on 05/Nov/19 $$=\underset{\mathrm{i}=\mathrm{1}}…
Question Number 73027 by mathmax by abdo last updated on 05/Nov/19 $${x}\:{and}\:{y}\:{are}\:{reals}\left({or}\:{complex}\right)\:{let}\:{put}\:{x}^{\left(\mathrm{0}\right)} =\mathrm{1}\:,{x}^{\left(\mathrm{1}\right)} ={x} \\ $$$${x}^{\left(\mathrm{2}\right)} ={x}\left({x}−\mathrm{1}\right)…..{x}^{\left({n}\right)} ={x}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)…\left({x}−{n}+\mathrm{1}\right){prove}\:{that} \\ $$$$\left({x}+{y}\right)^{\left({n}\right)} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:\:{x}^{\left({n}−{k}\right)}…
Question Number 73021 by TawaTawa last updated on 05/Nov/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 7478 by Yozzia last updated on 31/Aug/16 $${Find}\:{the}\:{value}\:{of}\:\:{x}^{\mathrm{3}} \left({x}^{\mathrm{3}} −\mathrm{18}\right)\:\:{if}\:\:{x}\left({x}−\mathrm{3}\right)=−\mathrm{1}. \\ $$ Answered by Rasheed Soomro last updated on 31/Aug/16 $$\:\:\:{x}^{\mathrm{3}} \left({x}^{\mathrm{3}} −\mathrm{18}\right)\:\:{if}\:\:{x}\left({x}−\mathrm{3}\right)=−\mathrm{1}…