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Question-223449

Question Number 223449 by ajfour last updated on 25/Jul/25 Answered by ajfour last updated on 26/Jul/25 $$\:\:\:\sqrt{\mathrm{1}−\theta^{\mathrm{2}} }=\frac{\mathrm{sin}\:\left(\phi−\theta\right)}{\mathrm{sin}\:\phi} \\ $$$${Wow}!\:\:\:\:\:\:{arc}\:{CD}=\:{line}\:{AB} \\ $$$$ \\ $$$$\bullet\:{Find}\:{CT}/{AO}={t}/{R}\:\:{in}\:{terms}\:{of}\:\theta. \\…

Question-223405

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} \\…

Good-day-great-problem-solvers-Please-I-need-links-to-resources-helpful-for-preparations-for-Olympiad-mathematics-especially-books-and-video-recommendations-I-ll-be-grateful-to-get-our-responses-

Question Number 223412 by nECxx2 last updated on 24/Jul/25 $${Good}\:{day}\:{great}\:{problem}\:{solvers}. \\ $$$${Please}\:{I}\:{need}\:{links}\:{to}\:{resources}\:{helpful} \\ $$$${for}\:{preparations}\:{for}\:{Olympiad}\:{mathematics} \\ $$$${especially}\:{books}\:{and}\:{video}\:{recommendations}. \\ $$$${I}'{ll}\:{be}\:{grateful}\:{to}\:{get}\:{our}\:{responses}. \\ $$ Commented by fantastic last updated…

is-it-possible-to-prove-that-mn-m-n-m-n-divisible-by-6-always-

Question Number 223414 by BaliramKumar last updated on 24/Jul/25 $${is}\:{it}\:{possible}\:{to}\:{prove}\:{that}\:{mn}\left({m}+{n}\right)\left({m}−{n}\right)\: \\ $$$${divisible}\:{by}\:\mathrm{6}\:{always}\:\:\:\:\:\:\:\:\:\: \\ $$ Answered by mehdee7396 last updated on 24/Jul/25 $${let}\:\:\:{d}={mn}\left({m}+{n}\right)\left({m}−{n}\right) \\ $$$${case}\mathrm{1} \\…