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Category: Algebra

one-solution-of-the-equation-x-a-x-b-x-c-x-d-9-is-x-2-If-a-b-c-d-are-different-integers-then-a-b-c-d-

Question Number 196450 by cortano12 last updated on 25/Aug/23 $$\mathrm{one}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\:\left(\mathrm{x}−\mathrm{a}\right)\left(\mathrm{x}−\mathrm{b}\right)\left(\mathrm{x}−\mathrm{c}\right)\left(\mathrm{x}−\mathrm{d}\right)\:=\:\mathrm{9}\: \\ $$$$\:\mathrm{is}\:\mathrm{x}=\mathrm{2}.\:\mathrm{If}\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\:\mathrm{are}\:\mathrm{different}\: \\ $$$$\:\mathrm{integers}\:\mathrm{then}\:\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}\:=?\: \\ $$ Answered by Rasheed.Sindhi last updated on 25/Aug/23…

find-the-minimum-value-of-f-x-f-x-x-2-2x-5-4x-2-4x-10-

Question Number 196343 by universe last updated on 23/Aug/23 $$\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}\:+\mathrm{5}}\:\:+\:\:\sqrt{\mathrm{4x}^{\mathrm{2}} \:−\mathrm{4x}\:+\mathrm{10}\:} \\ $$ Answered by MM42 last updated on 23/Aug/23 $$\sqrt{\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{4}}+\sqrt{\left(\mathrm{2}{x}−\mathrm{1}\right)^{\mathrm{2}}…

log-5-5-5-5-5-

Question Number 196355 by MATHEMATICSAM last updated on 23/Aug/23 $$\mathrm{log}_{\mathrm{5}} \sqrt{\mathrm{5}\sqrt{\mathrm{5}\sqrt{\mathrm{5}\sqrt{\mathrm{5}…..}}}\:}=\:? \\ $$ Commented by bbbbbbbb last updated on 23/Aug/23 $$\mathrm{log}_{\mathrm{5}} \sqrt{\mathrm{5}\sqrt{\mathrm{5}\sqrt{\mathrm{5}\sqrt{\mathrm{5}…..}}}\:}=\:? \\ $$$$\sqrt{\mathrm{x}\sqrt{\mathrm{x}\sqrt{\mathrm{x}\sqrt{\mathrm{x}…..}}}}=\mathrm{x} \\…

If-n-N-and-n-2-Then-tan-1-n-1-k-2-n-arctan-1-k-lt-2-5-n-1-

Question Number 196300 by hardmath last updated on 22/Aug/23 $$\mathrm{If}\:\rightarrow\:\mathrm{n}\:\in\:\mathbb{N}\:\:\:\:\:\mathrm{and}\:\:\:\:\:\mathrm{n}\:\geqslant\:\mathrm{2} \\ $$$$\mathrm{Then}\:\rightarrow\:\mathrm{tan}\:\left(\frac{\mathrm{1}}{\mathrm{n}\:−\:\mathrm{1}}\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{2}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{k}}\right)\:<\:\frac{\mathrm{2}}{\mathrm{5}}\:+\:\frac{\boldsymbol{\gamma}}{\mathrm{n}\:−\:\mathrm{1}} \\ $$ Answered by sniper237 last updated on 22/Aug/23 $${n}=\mathrm{2}\Rightarrow\mathrm{0},\mathrm{5}={tan}\left({arctan}\left(\mathrm{1}/\mathrm{2}\right)\right)\overset{?} {<}\mathrm{2}/\mathrm{5}\:=\mathrm{0},\mathrm{4}\:…