Question Number 223487 by Tawa11 last updated on 26/Jul/25 Let Φ be the hyperbola xy = b², b ≠ 0, and P be a point…
Question Number 223483 by fantastic last updated on 26/Jul/25 $$\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)=\mathrm{1} \\ $$$$\left({x}−\mathrm{1}\right)^{\mathrm{15}} −\frac{\mathrm{1}}{\left({x}−\mathrm{1}\right)^{\mathrm{15}} }=?? \\ $$ Answered by mr W last updated on 26/Jul/25 $${let}\:{t}={x}−\mathrm{1}…
Question Number 223474 by fantastic last updated on 26/Jul/25 $$\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+{x}}}=\sqrt[{\mathrm{3}}]{{x}} \\ $$ Commented by fantastic last updated on 26/Jul/25 $$\sqrt{{a}+\sqrt{{a}+{x}}}=\sqrt[{\mathrm{3}}]{{x}} \\ $$$${let}\:{t}=\sqrt[{\mathrm{3}}]{{x}} \\ $$$${So}\:{the}\:{equation}\:{becomes} \\…
Question Number 223459 by mr W last updated on 26/Jul/25 $${solve}\:{for}\:{x}\in{R} \\ $$$$\sqrt{\mathrm{25}−\mathrm{10}{x}−{x}^{\mathrm{2}} }+\sqrt{\mathrm{15}−{x}^{\mathrm{2}} }=\mathrm{2}\sqrt{\mathrm{5}} \\ $$ Answered by fantastic last updated on 26/Jul/25 $$\sqrt{\mathrm{25}−\mathrm{10}{x}−{x}^{\mathrm{2}}…
Question Number 223429 by klipto last updated on 25/Jul/25 $$…. \\ $$ Commented by klipto last updated on 25/Jul/25 Answered by Rasheed.Sindhi last updated on…
Question Number 223424 by behi834171 last updated on 25/Jul/25 Commented by fantastic last updated on 25/Jul/25 $${GIGANTIC}\:{when}\:{using}\:{normal}\:{method} \\ $$ Commented by Ghisom last updated on…
Question Number 223405 by behi834171 last updated on 24/Jul/25 Answered by fantastic last updated on 24/Jul/25 $$\sqrt[{\mathrm{3}}]{{x}+\sqrt[{\mathrm{3}}]{{x}+\mathrm{1}}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left(\sqrt[{\mathrm{3}}]{{x}+\sqrt[{\mathrm{3}}]{{x}+\mathrm{1}}}\right)^{\mathrm{3}} =\frac{\mathrm{1}}{\mathrm{8}} \\ $$$$\therefore{x}+\sqrt[{\mathrm{3}}]{{x}+\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{8}} \\ $$$${let}\:\sqrt[{\mathrm{3}}]{{x}+\mathrm{1}}={u} \\…
Question Number 223403 by Rojarani last updated on 24/Jul/25 Commented by mr W last updated on 24/Jul/25 $${should}\:{be}\:\:…=+\:\sqrt[{\mathrm{3}}]{\mathrm{3}\sqrt[{\mathrm{3}}]{\mathrm{37}}−\mathrm{10}} \\ $$ Answered by mr W last…
Question Number 223400 by behi834171 last updated on 23/Jul/25 $$\boldsymbol{{f}}\left(\mathrm{1}\right)=\mathrm{2025} \\ $$$$\underset{\mathrm{1}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\sum}}{f}}\left(\boldsymbol{{k}}\right)=\boldsymbol{{n}}^{\mathrm{2}} .\boldsymbol{{f}}\left(\boldsymbol{{n}}\right) \\ $$$$\boldsymbol{{f}}\left(\mathrm{2025}\right)=? \\ $$ Answered by mr W last updated…
Question Number 223386 by behi834171 last updated on 23/Jul/25 Answered by mr W last updated on 23/Jul/25 $${still}\:{using}\:{my}\:{method}\:{generally}\:{for} \\ $$$$\boldsymbol{{x}}^{\boldsymbol{{n}}} +\boldsymbol{{kx}}+\boldsymbol{{p}}=\mathrm{0} \\ $$$${x}^{{n}} −{a}=−{k}\left({x}+\frac{{p}+{a}}{{k}}\right)=−{ky} \\…