Question Number 165321 by amin96 last updated on 29/Jan/22 Answered by mahdipoor last updated on 31/Jan/22 $$\begin{cases}{{u}^{\mathrm{2}} +\mathrm{2}{u}+\mathrm{4}\overset{{u}={x}} {\Rightarrow}={x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}}\\{{u}^{\mathrm{2}} −\mathrm{2}{u}+\mathrm{4}\overset{{u}={x}+\mathrm{2}} {\Rightarrow}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}}\end{cases}\Rightarrow \\ $$$$\underset{{i}={u}}…
Question Number 164628 by amin96 last updated on 19/Jan/22 $$\mathrm{60}!=\underline{\boldsymbol{\mathrm{abc}}\ldots\boldsymbol{\mathrm{nm}}\mathrm{000}\ldots\mathrm{0}} \\ $$$$\boldsymbol{\mathrm{m}}=?\:\:\boldsymbol{\mathrm{n}}=? \\ $$ Commented by amin96 last updated on 20/Jan/22 $$\boldsymbol{\mathrm{answer}}\:\mathrm{9};\:\mathrm{6} \\ $$$$ \\…
Question Number 33551 by Rasheed.Sindhi last updated on 19/Apr/18 Commented by Rasheed.Sindhi last updated on 19/Apr/18 $$\mathrm{Question}#\mathrm{10000}\left(\mathrm{by}\:\mathrm{tawakalitu}\right)\:\mathrm{reposted} \\ $$ Answered by MJS last updated on…
Question Number 98806 by bemath last updated on 16/Jun/20 $$\mathrm{for}\:{a}\:\mathrm{is}\:\mathrm{integer}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mid\mid{x}−\mathrm{1}\mid\:−\mathrm{2}\mid\:\leqslant\:{a}\:\:\mathrm{exactly}\:\mathrm{has}\:\mathrm{2013} \\ $$$$\mathrm{solution} \\ $$ Commented by Rasheed.Sindhi last updated on 16/Jun/20 $${Assuming}\:{x}\:{an}\:{integer}: \\…
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Question Number 163939 by Rasheed.Sindhi last updated on 12/Jan/22 $$\mathrm{An}\:\mathrm{old}\:\mathrm{unsolved}\:\mathrm{question}#\mathrm{1132} \\ $$$$\mathrm{let}\:\mathrm{S}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\right\},\:\mathrm{if}\:\mathrm{A},\mathrm{B},\mathrm{C}\:\mathrm{is}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{A}\cap\mathrm{B}\cap\mathrm{C}=\varnothing \\ $$$$\mathrm{A}\cap\mathrm{B}\neq\varnothing \\ $$$$\mathrm{A}\cap\mathrm{C}\neq\varnothing \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{be}\:\mathrm{choose}\:\mathrm{A},\mathrm{B}\:\mathrm{and} \\ $$$$\mathrm{C} \\ $$ Terms…
Question Number 163735 by amin96 last updated on 09/Jan/22 Commented by mr W last updated on 11/Jan/22 $${i}\:{think}\:{question}\:{is}\:{wrong}. \\ $$$${c}\:{can}\:{be}\:{any}\:{value}\:{except}\:\mathrm{2}. \\ $$$${c}_{{min}} =−\infty,\:{c}_{{max}} =+\infty \\…
Question Number 163435 by amin96 last updated on 06/Jan/22 Answered by Mathspace last updated on 07/Jan/22 $${S}=\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{\mathrm{4}{n}+\mathrm{1}}\left(\frac{\mathrm{1}}{\mathrm{4}{n}+\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}{n}+\mathrm{4}}\right) \\ $$$$=\sum_{{m}=\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{\left(\mathrm{4}{n}+\mathrm{1}\right)\left(\mathrm{4}{n}+\mathrm{3}\right)} \\ $$$$−\sum_{{n}=\mathrm{0}}…
Question Number 163161 by kdaramaths last updated on 04/Jan/22 Answered by JDamian last updated on 05/Mar/23 $$\mathrm{there}\:\mathrm{is}\:\mathrm{no}\:\beta\:\:\mathrm{satisfying}\:\mathrm{those}\:\mathrm{constraints} \\ $$$$ \\ $$$${n}=\mathrm{5}^{\alpha} \mathrm{119}^{\beta} =\mathrm{5}^{\alpha} \mathrm{7}^{\beta} \mathrm{17}^{\beta}…
Question Number 97438 by john santu last updated on 08/Jun/20 $$\mathrm{If}\:−\mathrm{3}\leqslant\mathrm{x}\leqslant\mathrm{4},\:−\mathrm{2}\leqslant\mathrm{y}\leqslant\mathrm{5},\:\mathrm{4}\leqslant\mathrm{z}\leqslant\mathrm{10} \\ $$$$,\:\mathrm{find}\:\mathrm{the}\:\mathrm{greatest} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{w}\:=\:\mathrm{z}−\mathrm{xy}\: \\ $$ Commented by bemath last updated on 08/Jun/20 $$\mathrm{for}\:\mathrm{xy}\:=\:−\mathrm{15}\:\mathrm{and}\:\mathrm{z}\:=\:\mathrm{10}…