Question Number 113211 by bemath last updated on 11/Sep/20 $$\mathrm{If}\:\alpha\:\mathrm{is}\:\mathrm{a}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{4x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{1}=\mathrm{0}\:.\:\mathrm{How}\:\mathrm{do}\:\mathrm{you} \\ $$$$\mathrm{prove}\:\mathrm{the}\:\mathrm{other}\:\mathrm{root}\:\mathrm{is} \\ $$$$\mathrm{4}\alpha^{\mathrm{3}} −\mathrm{3}\alpha\:?\: \\ $$ Answered by 1549442205PVT last updated…
Question Number 112507 by bemath last updated on 08/Sep/20 Answered by mr W last updated on 09/Sep/20 $$\frac{\mathrm{1}}{{A}}+\frac{\mathrm{1}}{{B}}=\frac{\mathrm{1}}{\mathrm{35}} \\ $$$$\frac{\mathrm{5}}{\mathrm{7}}{A}+\frac{\mathrm{2}}{\mathrm{7}}{B}=\mathrm{90} \\ $$$$\mathrm{5}{A}^{\mathrm{2}} −\mathrm{735}{A}+\mathrm{630}×\mathrm{35}=\mathrm{0} \\ $$$${A}=\frac{\mathrm{735}\pm\mathrm{315}}{\mathrm{10}}=\mathrm{105}\:{or}\:\mathrm{42}…
Question Number 46631 by Meritguide1234 last updated on 29/Oct/18 Commented by Meritguide1234 last updated on 31/Oct/18 $${what}\:{wrong}? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 110504 by Rio Michael last updated on 29/Aug/20 $$\mathrm{Given}\:\mathrm{a}\:\mathrm{transformation}\:,\:\mathcal{T}:\:\mathbb{C}\:\rightarrow\:\mathbb{C}\:;\:{z}\:\rightarrow\:\omega \\ $$$$\:\mathrm{Show}\:\mathrm{that}\:\mathrm{if}\:\omega\:=\:\frac{{z}−{i}}{{z}\:+\mathrm{1}}\:\mathrm{then}\:{z}\:=\:\frac{\omega\:+\:{i}}{\mathrm{1}−\omega}.\:\mathrm{Hence} \\ $$$$\mathrm{the}\:\mathrm{image}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:\mid{z}−{i}\mid\:=\:\mid{z}\:+\:\mathrm{2}\mid\:\mathrm{under}\:\mathrm{the}\:\mathrm{transformation} \\ $$$$\mathcal{T}\:\:\:\:\mathrm{the}\:\omega−\mathrm{plane}\:\mathrm{is}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{center}\:\left(−\mathrm{2},−{i}\right)\:\mathrm{and}\:\mathrm{radius}\:\sqrt{\mathrm{10}}\:.\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 175923 by CrispyXYZ last updated on 09/Sep/22 $$\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{differences}\:\mathrm{among}\:“\:{if}\:'',\:“\:{only}\:\:{if}\:''\:\mathrm{and}\:“\:{if}\:\:{and}\:\:{only}\:\:{if}\:''? \\ $$ Answered by Vynho last updated on 09/Sep/22 $${if}={necessary}\:{condition} \\ $$$${only}\:{if}\:=\:{sufficient}\:{condition} \\ $$$${if}\:{and}\:{only}\:{if}={necessary}\:{and}\:{sufficient}\:{condition} \\…
Question Number 44584 by Joel578 last updated on 01/Oct/18 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:\:{a},\:{b},\:{c}\:\in\:\mathbb{Z}\:\:\mathrm{and}\:\:{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:=\:{c}^{\mathrm{2}} ,\:\mathrm{then} \\ $$$$\mathrm{3}\:\mid\:{ab} \\ $$ Commented by ajfour last updated on 02/Oct/18 $${then}\:\:\mathrm{3}\mid{ab}\:\:\:{means}\:?!..…
Question Number 175017 by oustmuchiya@gmail.com last updated on 16/Aug/22 Commented by TheHoneyCat last updated on 16/Aug/22 $$\mathrm{Not}\:\mathrm{sure}\:\mathrm{I}\:\mathrm{get}\:\mathrm{the}\:\mathrm{question}… \\ $$$$\mathrm{what}\:\mathrm{is}\:“\mathrm{A}\alpha''? \\ $$$$\mathrm{Is}\:\mathrm{A}\:\mathrm{a}\:\mathrm{function}? \\ $$$$\mathrm{Or}\:\mathrm{a}\:\mathrm{set}\:\left(\mathrm{then}\:\mathrm{is}\:\mathrm{it}\:\mathrm{the}\:\mathrm{product}\:\mathrm{with}\:\alpha\:\mathrm{and}\:\mathrm{if}\right. \\ $$$$\left.\mathrm{so}\:\mathrm{wath}\:\mathrm{product}…\:\mathrm{is}\:\Omega\subset\mathbb{C}?\right)…
Question Number 107433 by Adilali last updated on 10/Aug/20 $$\int{x}^{{x}} {dx}=? \\ $$ Answered by Dwaipayan Shikari last updated on 10/Aug/20 $$\int{e}^{{xlogx}} {dx} \\ $$$$\int{e}^{{t}}…
Question Number 106628 by deep last updated on 06/Aug/20 $$\frac{\left(\boldsymbol{{p}}−\mathrm{1}\right)}{\boldsymbol{{p}}}\:\:\:\:\:\:\boldsymbol{{where}}\:\boldsymbol{{p}}=\boldsymbol{{prime}}\:\boldsymbol{{no}}. \\ $$$$\boldsymbol{{R}}{emainder}\:{will}\:{always}\:{be}\:\left({p}−\mathrm{1}\right)\:{or}\:−\mathrm{1} \\ $$$$ \\ $$$$ \\ $$$${Que}.\:{find}\:{Remainder} \\ $$$$\frac{\mathrm{1}!+\mathrm{2}!+\mathrm{3}!+……………………\mathrm{1000}!}{\mathrm{10}} \\ $$$${Que}. \\ $$$$\frac{\mathrm{1}!+\mathrm{2}!+\mathrm{3}!+……………………\mathrm{1000}!}{\mathrm{12}} \\…
Question Number 171829 by Mikenice last updated on 21/Jun/22 $${please}\:{i}\:{need}\:{cubic}\:{formula} \\ $$$$ \\ $$ Answered by MathematicalUser2357 last updated on 05/Jan/24 $${x}_{\mathrm{1}} =−\frac{{b}}{\mathrm{3}{a}}−\frac{\mathrm{1}}{\mathrm{3}{a}}\sqrt[{\mathrm{3}}]{\frac{\mathrm{2}{b}^{\mathrm{3}} −\mathrm{9}{abc}+\mathrm{27}{a}^{\mathrm{2}} {d}+\sqrt{\left(\mathrm{2}{b}^{\mathrm{3}}…