Question Number 181722 by Agnibhoo98 last updated on 29/Nov/22 $$\mathrm{Prove}\:\mathrm{that}, \\ $$$$\left(\frac{\mathrm{1}}{{a}\:−\:{b}}\:+\:\frac{\mathrm{1}}{{b}\:−\:{c}}\:+\:\frac{\mathrm{1}}{{c}\:−\:{a}}\right)^{\mathrm{2}} \:=\: \\ $$$$\frac{\mathrm{1}}{\left({a}\:−\:{b}\right)^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\left({b}\:−\:{c}\right)^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\left({c}\:−\:{a}\right)^{\mathrm{2}} } \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 116113 by Lordose last updated on 01/Oct/20 $$\boldsymbol{\mathrm{what}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{exponent}}\:\boldsymbol{\mathrm{of}}\:\mathrm{12}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{expansion}}\:\boldsymbol{\mathrm{of}}\:\mathrm{100}! \\ $$ Answered by mr W last updated on 01/Oct/20 $$\mathrm{12}=\mathrm{2}^{\mathrm{2}} ×\mathrm{3} \\…
Question Number 50445 by ANTARES VY last updated on 16/Dec/18 $$\boldsymbol{\mathrm{The}}\:\:\boldsymbol{\mathrm{roots}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{fallowing}} \\ $$$$\boldsymbol{\mathrm{functions}}\:\:\boldsymbol{\mathrm{are}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{Sequences}}\:\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{arithmetic}}\:\:\boldsymbol{\mathrm{progressiyon}} \\ $$$$\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\boldsymbol{\mathrm{x}}^{\mathrm{5}} −\mathrm{20}\boldsymbol{\mathrm{x}}^{\mathrm{4}} +\boldsymbol{\mathrm{ax}}^{\mathrm{3}} +\boldsymbol{\mathrm{bx}}^{\mathrm{2}} +\boldsymbol{\mathrm{cx}}+\mathrm{24} \\ $$$$\boldsymbol{\mathrm{f}}\left(\mathrm{8}\right)=? \\ $$…
Question Number 181484 by Linton last updated on 25/Nov/22 $${If}\:{a}\:{hen}\:{and}\:{a}\:{half} \\ $$$${lay}\:{an}\:{egg}\:{and}\:{a}\:{half} \\ $$$${in}\:{a}\:{day}\:{and}\:{a}\:{half} \\ $$$${how}\:{many}\:{eggs}\:{would} \\ $$$${one}\:{hen}\:{lay}\:{in}\:{one} \\ $$$${day}? \\ $$ Commented by MJS_new…
Question Number 115856 by bemath last updated on 29/Sep/20 $${Which}\:{is}\:{greater} \\ $$$${P}\:=\:\left(\mathrm{1983}\right)\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+…+\mathrm{1984}\right)\:,\:{or} \\ $$$${Q}\:=\:\left(\mathrm{1984}\right)\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+…+\mathrm{1983}\right) \\ $$ Answered by bobhans last updated on 29/Sep/20 $${let}\:{z}\:=\:\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+…+\mathrm{1983} \\…
Question Number 50248 by peter frank last updated on 15/Dec/18 Answered by mr W last updated on 15/Dec/18 $${P}\left({p},\frac{{c}^{\mathrm{2}} }{{p}}\right) \\ $$$${Q}\left({q},\frac{{c}^{\mathrm{2}} }{{q}}\right) \\ $$$${PQ}=\sqrt{\left({p}−{q}\right)^{\mathrm{2}}…
Question Number 181275 by Linton last updated on 23/Nov/22 $${what}\:{is}\:{the}\:{sum}\:{of}\:{all} \\ $$$${even}\:{factors}\:{of}\:\mathrm{1000}? \\ $$ Commented by Rasheed.Sindhi last updated on 24/Nov/22 ���� Commented by Linton…
Question Number 50135 by peter frank last updated on 14/Dec/18 Commented by maxmathsup by imad last updated on 01/Jan/19 $${let}\:{solve}\:\left(\mathrm{2}{x}−\mathrm{1}\right){y}^{''} \:−{y}^{'} =\mathrm{0}\:\:\:{withy}\left(\mathrm{0}\right)=\mathrm{2}\:{and}\:{y}^{'} \left(\mathrm{0}\right)=\mathrm{3}\:\:{let}\:{use}\:{changement} \\ $$$${y}^{'}…
Question Number 181039 by depressiveshrek last updated on 20/Nov/22 $${Prove}\:{that}\:{for}\:{all}\:{a}^{\mathrm{2}} \:{divisible}\:{by}\:{b}, \\ $$$${a}\:{is}\:{also}\:{divisible}\:{by}\:{b} \\ $$$${for}\:{all}\:{a},\:{b}\:\in\:\mathbb{N} \\ $$ Commented by mr W last updated on 20/Nov/22…
Question Number 180828 by Vynho last updated on 17/Nov/22 $${H}_{{n}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…+\frac{\mathrm{1}}{{n}} \\ $$$${H}_{\mathrm{2}{n}} =?\:{compute}\:{H}_{\mathrm{2}{n}} −{H}_{{n}} \:{and}\:{H}_{{n}+\mathrm{1}} −{H}_{{n}} \\ $$ Commented by Frix last updated on…