Question Number 110471 by abdullahquwatan last updated on 29/Aug/20 $$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{x}\:\mathrm{values} \\ $$$$\left({x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{9}\right)^{\frac{{x}−\mathrm{3}}{{x}−\mathrm{1}}} \:=\:\left({x}−\mathrm{3}\right)^{\left({x}−\mathrm{4}\right)} \\ $$ Answered by Rasheed.Sindhi last updated on 29/Aug/20 $$\left({x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{9}\right)^{\frac{{x}−\mathrm{3}}{{x}−\mathrm{1}}}…
Question Number 110463 by Rio Michael last updated on 29/Aug/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{gcd}\left({n}−\mathrm{1},{n}+\mathrm{1}\right) \\ $$ Commented by mr W last updated on 29/Aug/20 $${if}\:{n}={odd}\:{then}\:{gcd}\left({n}−\mathrm{1},{n}+\mathrm{1}\right)=\mathrm{2} \\ $$$${if}\:{n}={even}\:{then}\:{gcd}\left({n}−\mathrm{1},{n}+\mathrm{1}\right)=\mathrm{1} \\…
Question Number 44918 by Tawa1 last updated on 06/Oct/18 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{of}:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{2}.\mathrm{3}}\:+\:\frac{\mathrm{3}}{\mathrm{2}.\mathrm{3}.\mathrm{4}}\:+\:\frac{\mathrm{5}}{\mathrm{3}.\mathrm{4}.\mathrm{5}}\:+\:…\: \\ $$ Commented by maxmathsup by imad last updated on 06/Oct/18 $${let}\:\:{S}\:=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{2}{n}−\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)}\:\:{we}\:{have}\:{S}\:=\frac{\mathrm{1}}{\mathrm{1}.\mathrm{2}.\mathrm{3}}\:+\frac{\mathrm{3}}{\mathrm{2}.\mathrm{3}.\mathrm{4}}\:+… \\…
Question Number 110436 by bemath last updated on 29/Aug/20 $$\:\:\:\:\:\mathrm{If}\:\mathrm{2f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:=\:\mathrm{3x} \\ $$$$\:\:\:\:\:\mathrm{what}\:\mathrm{is}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$ Answered by john santu last updated on 29/Aug/20 $$\:\:\:{replace}\:{x}\:{by}\:\frac{\mathrm{1}}{{x}} \\ $$$$\Leftrightarrow\:\mathrm{2}{f}\left(\frac{\mathrm{1}}{{x}}\right)\:+\:{f}\left({x}\right)\:=\:\frac{\mathrm{3}}{{x}}\:…
Question Number 110434 by Aina Samuel Temidayo last updated on 29/Aug/20 $$\mathrm{The}\:\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{four}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an} \\ $$$$\mathrm{increasing}\:\mathrm{arithmetic}\:\mathrm{progression}\:\mathrm{is}\:\mathrm{a}, \\ $$$$\mathrm{their}\:\mathrm{sum}\:\mathrm{is}\:\mathrm{b},\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{their} \\ $$$$\mathrm{reciprocal}\:\mathrm{is}\:\mathrm{c}.\:\mathrm{Suppose}\:\mathrm{that}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{form} \\ $$$$\mathrm{a}\:\mathrm{geometric}\:\mathrm{progression}\:\mathrm{whose} \\ $$$$\mathrm{product}\:\mathrm{is}\:\mathrm{8000},\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{first}\:\mathrm{and}\:\mathrm{fourth}\:\mathrm{term}. \\…
Question Number 44898 by ajfour last updated on 06/Oct/18 $${If}\:\:\:\:{x}^{\mathrm{4}} +{px}^{\mathrm{3}} +{qx}^{\mathrm{2}} +{rx}+\mathrm{5}\:=\:\mathrm{0} \\ $$$${has}\:{four}\:{real}\:{roots},\:{then}\:{find} \\ $$$$\:{the}\:{minimum}\:{value}\:{of}\:\boldsymbol{{pr}}. \\ $$ Commented by MJS last updated on…
Question Number 44892 by Tawa1 last updated on 06/Oct/18 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{formular}\:\mathrm{for}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{kth}\:\mathrm{power}\:\mathrm{of}\:\mathrm{natural}\:\mathrm{number} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 06/Oct/18 $${do}\:{the}\:{question}\:{mean} \\ $$$${S}_{{k}} =\mathrm{1}^{{k}} +\mathrm{2}^{{k}} +\mathrm{3}^{{k}}…
Question Number 110425 by Aina Samuel Temidayo last updated on 28/Aug/20 $$ \\ $$$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{not}\:\mathrm{a}\:\mathrm{factor} \\ $$$$\mathrm{of}\:\mathrm{x}^{\mathrm{6}} −\mathrm{56x}+\mathrm{55} \\ $$$$\mathrm{A}.\:\mathrm{x}−\mathrm{1}\:\mathrm{B}.\:\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{5}\:\mathrm{C}. \\ $$$$\mathrm{x}^{\mathrm{3}} +\mathrm{2x}^{\mathrm{2}} −\mathrm{2x}−\mathrm{11}\:\mathrm{D}. \\…
Question Number 175959 by BaliramKumar last updated on 10/Sep/22 $${f}\left({x}\right)\:=\:{x}^{\mathrm{6}} \:−\:\mathrm{100}{x}^{\mathrm{5}} \:+\:\mathrm{100}{x}^{\mathrm{4}} \:−\:\mathrm{100}{x}^{\mathrm{3}} \:+\:\mathrm{100}{x}^{\mathrm{2}} \:−\:\mathrm{100}{x}\:+\:\mathrm{100} \\ $$$${f}\left(\mathrm{99}\right)\:=\:? \\ $$ Commented by infinityaction last updated on…
Question Number 110420 by Aina Samuel Temidayo last updated on 28/Aug/20 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{x}^{\mathrm{5}} −\mathrm{3x}^{\mathrm{4}} −\mathrm{17x}^{\mathrm{3}} −\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{17}\:\mathrm{cannot}\:\mathrm{be} \\ $$$$\mathrm{factorized}\:\mathrm{completely}\:\mathrm{over}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of} \\ $$$$\mathrm{polynomials}\:\mathrm{with}\:\mathrm{integral}\:\mathrm{coefficients}. \\ $$ Answered…