Question Number 33843 by prof Abdo imad last updated on 25/Apr/18 $${decompose}\:{inside}\:{R}\left({x}\right)\:{the}\:{fraction} \\ $$$${F}\left({x}\right)=\:\:\frac{\mathrm{1}}{\left({x}+\mathrm{3}\right)^{{n}} \:\left({x}+\mathrm{1}\right)}\:{with}\:{n}\:{integr}\:. \\ $$ Commented by abdo imad last updated on 28/Apr/18…
Question Number 33837 by NECx last updated on 25/Apr/18 $${find}\:{y}\:{if}\:\mid\frac{{y}−\mathrm{3}}{{y}+\mathrm{1}}\mid<\mathrm{2} \\ $$$$ \\ $$$${i}\:{mean}\:{modulus}\:{by}\:\mid \\ $$ Answered by Rasheed.Sindhi last updated on 26/Apr/18 $${find}\:{y}\:{if}\:\mid\frac{{y}−\mathrm{3}}{{y}+\mathrm{1}}\mid<\mathrm{2} \\…
Question Number 33838 by NECx last updated on 25/Apr/18 $${Find}\:{the}\:{values}\:{of}\:{k}\:{if}\:\frac{{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{4}}{\mathrm{5}{x}−{k}}\: \\ $$$${may}\:{be}\:{capable}\:{of}\:{taking}\:{on}\:{all} \\ $$$${values}\:{when}\:{x}\:{is}\:{real}. \\ $$ Answered by MJS last updated on 26/Apr/18 $$\mathrm{we}\:\mathrm{have}\:\mathrm{to}\:\mathrm{get}\:\mathrm{rid}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}……
Question Number 33836 by NECx last updated on 25/Apr/18 $${for}\:{what}\:{values}\:{of}\:{x}\:{if} \\ $$$$\frac{{x}\left({x}−\mathrm{1}\right)}{\mathrm{2}{x}+\mathrm{3}}>\mathrm{0} \\ $$ Answered by Rasheed.Sindhi last updated on 26/Apr/18 $$\frac{{x}\left({x}−\mathrm{1}\right)}{\mathrm{2}{x}+\mathrm{3}}>\mathrm{0\begin{cases}{{x}\left({x}−\mathrm{1}\right)>\mathrm{0}\:\wedge\:\mathrm{2}{x}+\mathrm{3}>\mathrm{0}…\mathrm{A}}\\{{x}\left({x}−\mathrm{1}\right)<\mathrm{0}\:\wedge\:\mathrm{2}{x}+\mathrm{3}<\mathrm{0}….\mathrm{B}}\end{cases}} \\ $$$$\mathrm{A}\::\:\:{x}>\mathrm{0}\:\wedge\:{x}−\mathrm{1}>\mathrm{0} \\…
Question Number 33834 by uddipan last updated on 25/Apr/18 $${P}\left({x}\right)={x}^{{n}} +{a}_{{n}−\mathrm{1}} {x}^{{n}−\mathrm{1}} +….\:{a}_{\mathrm{1}} {x}+{a}_{\mathrm{0}} \:\:\:{be}\:{a}\:{polynomial}\:{with}\:{all}\:{the}\:{real}\:{roots}, \\ $$$${prove}\:{that}\:\:\:\:\:\:\:\:\:\left({n}−\mathrm{1}\right){a}_{{n}−\mathrm{1}} ^{\mathrm{2}} \:\geqslant\:\mathrm{2}{na}_{{n}−\mathrm{2}} \:\:. \\ $$ Terms of Service…
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Question Number 33805 by pieroo last updated on 25/Apr/18 $$\mathrm{The}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:\mathrm{and}\:\mathrm{a}\:\mathrm{rectangle}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{same}.\:\mathrm{The}\:\mathrm{width}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle}\:\mathrm{is}\:\mathrm{6}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{its}\:\mathrm{area} \\ $$$$\mathrm{is}\:\mathrm{16}\:\mathrm{cm}^{\mathrm{2}} \:\mathrm{less}\:\mathrm{than}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}. \\ $$ Answered by MJS last updated on…
Question Number 164875 by HongKing last updated on 22/Jan/22 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{natural}\:\mathrm{numbers}: \\ $$$$\boldsymbol{\varphi}\left(\boldsymbol{\mathrm{n}}\right)\:\centerdot\:\boldsymbol{\varphi}\left(\boldsymbol{\mathrm{n}}\:+\:\mathrm{1}\right)\:=\:\mathrm{288}\boldsymbol{\mathrm{n}} \\ $$$$\boldsymbol{\varphi}-\mathrm{Euler}'\mathrm{s}\:\mathrm{totient}\:\mathrm{function} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 164856 by Zaynal last updated on 22/Jan/22 $$\:\:\:\:\boldsymbol{\mathrm{Let}}\:\boldsymbol{{a}},\boldsymbol{{b}},\boldsymbol{{c}}\:>\mathrm{0}; \\ $$$$\:\:\:\:\mathrm{42}\boldsymbol{{abc}}\:+\:\mathrm{4}\boldsymbol{{bca}}\:+\mathrm{1}\boldsymbol{{cab}}\:\leqslant\:\mathrm{24} \\ $$$$\:\:\:\:\mathrm{T}\boldsymbol{\mathrm{hen}}\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{ab}}}\:+\:\frac{\mathrm{2}}{\boldsymbol{\mathrm{bc}}}\:+\:\frac{\mathrm{3}}{\boldsymbol{\mathrm{ca}}}\:=\:?? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:^{\left\{{Z}.\mathrm{A}\right\}} \\ $$ Commented by MJS_new last updated on 24/Jan/22…
Question Number 99319 by M±th+et+s last updated on 20/Jun/20 $${solve} \\ $$$$\left({x}^{\mathrm{2}} −\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)−\mathrm{11}\left({x}−\frac{\mathrm{1}}{{x}}\right)=\mathrm{14} \\ $$ Answered by behi83417@gmail.com last updated on 20/Jun/20 $$\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}=\mathrm{t}\Rightarrow\left(\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{2}} =\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{2}}…