Question Number 155206 by mathdanisur last updated on 26/Sep/21 $$\mathrm{Determine}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\mathrm{a};\mathrm{b};\mathrm{c};\mathrm{d};\mathrm{x};\mathrm{y};\mathrm{z};\mathrm{t}\:\:\mathrm{and}\:\:\mathrm{a}\neq\mathrm{b}\neq\mathrm{c}\neq\mathrm{d} \\ $$$$\mathrm{which}\:\mathrm{satisfy}\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{td}\:; \\ $$$$\mathrm{b}+\mathrm{c}+\mathrm{d}=\mathrm{xa}\:;\:\mathrm{c}+\mathrm{d}+\mathrm{a}=\mathrm{yb}\:;\:\mathrm{d}+\mathrm{a}+\mathrm{b}=\mathrm{zc} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 155189 by qaz last updated on 27/Sep/21 $$\mathrm{How}\:\mathrm{to}\:\mathrm{extract}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\:\mathrm{term}\:“\mathrm{x}^{\mathrm{n}} \mathrm{y}^{\mathrm{m}} \:''\:\:\mathrm{in}\:\left(\mathrm{1}+\frac{\mathrm{yx}}{\mathrm{1}−\mathrm{x}}\right)\left(\mathrm{1}−\frac{\mathrm{yx}}{\mathrm{1}−\mathrm{x}}\right)^{−\mathrm{1}} ? \\ $$ Answered by mr W last updated on 26/Sep/21 $$=\frac{\mathrm{1}−{x}+{xy}}{\mathrm{1}−{x}\left(\mathrm{1}+{y}\right)} \\…
Question Number 89653 by student work last updated on 18/Apr/20 Commented by john santu last updated on 18/Apr/20 $$\mathrm{2}^{{x}} \:=\:{p}\:\Rightarrow\:{p}^{\mathrm{3}} \:+\:{p}\:=\:\mathrm{16}\: \\ $$$${use}\:{Cardano}\:{method}\: \\ $$…
Question Number 155180 by mathdanisur last updated on 26/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 155182 by mathdanisur last updated on 26/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 155183 by mathdanisur last updated on 26/Sep/21 Answered by aleks041103 last updated on 26/Sep/21 $$\mathrm{1}−{tan}^{\mathrm{2}} \frac{{x}}{\mathrm{2}^{{k}} }=\frac{{cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}^{{k}} }−{sin}^{\mathrm{2}} \frac{{x}}{\mathrm{2}^{{k}} }}{{cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}^{{k}} }}=\frac{{cos}\frac{{x}}{\mathrm{2}^{{k}−\mathrm{1}}…
Question Number 155164 by mnjuly1970 last updated on 26/Sep/21 $$\:\:\:{solve}.. \\ $$$$\:\:\:\:\:\:\:\:\:\lfloor\:\frac{\:{x}}{\mathrm{2}+\:\sqrt{{x}}}\:\rfloor\:=\:\mathrm{3}\:\:\:\:\:\:\:\:\left(\:{x}\in\:\mathbb{Z}\:\right) \\ $$$$ \\ $$ Answered by MJS_new last updated on 26/Sep/21 $$\frac{{x}}{\mathrm{2}+\sqrt{{x}}}=\mathrm{3}\:\Rightarrow\:{x}\approx\mathrm{19}.\mathrm{11} \\…
Question Number 155154 by mathdanisur last updated on 26/Sep/21 $$\mathrm{let}\:\:\mathrm{n}\in\mathbb{N}^{+} \:\:\mathrm{solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{x}^{\mathrm{3}\boldsymbol{\mathrm{n}}} \:-\:\mathrm{y}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \:=\:\mathrm{y}^{\mathrm{3}\boldsymbol{\mathrm{n}}} \:-\:\mathrm{x}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \:=\:\mathrm{4} \\ $$ Answered by MJS_new last updated on…
Question Number 155153 by mathdanisur last updated on 26/Sep/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{in}\:\mathbb{R} \\ $$$$\sqrt{\mathrm{2}\left(\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{x}\:+\:\mathrm{1}\right)}\:=\:\mathrm{1}\:+\:\sqrt{\mathrm{x}}\:-\:\mathrm{x} \\ $$ Answered by MJS_new last updated on 26/Sep/21 $$\sqrt{{x}}\in\mathbb{R}\:\Rightarrow\:{x}\geqslant\mathrm{0}\:\mathrm{but}\:\mathrm{it}'\mathrm{s}\:\mathrm{easy}\:\mathrm{to}\:\mathrm{see}\:{x}\neq\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{lhs}>\mathrm{0}\:\Rightarrow\:\mathrm{1}+\sqrt{{x}}−{x}>\mathrm{0}…
Question Number 155144 by mnjuly1970 last updated on 26/Sep/21 $$ \\ $$$$\:\:{how}\:{many}\:{integer}\:{solutions}\: \\ $$$$\:\:\:\:{are}\:{there}\:: \\ $$$$\:\:\:\:\lfloor\:\frac{\mathrm{1}}{\mathrm{2}+\sqrt{{x}}}\rfloor\:=\:\mathrm{3}\:\:\:\:\:\:\:\:\:\blacksquare \\ $$$$ \\ $$ Commented by mr W last…