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Category: Algebra

Question-226118

Question Number 226118 by Spillover last updated on 20/Nov/25 Answered by mr W last updated on 20/Nov/25 $$\mathrm{1}+\alpha+\beta+\gamma+\alpha\beta+\beta\gamma+\gamma\alpha+\alpha\beta\gamma=\mathrm{33} \\ $$$$\mathrm{1}+\mathrm{6}+\alpha\beta+\beta\gamma+\gamma\alpha+\alpha\beta\gamma=\mathrm{33} \\ $$$$\alpha\beta+\beta\gamma+\gamma\alpha+\alpha\beta\gamma=\mathrm{26}\:\:\:…\left({i}\right) \\ $$$$\left(\alpha+\beta+\gamma\right)^{\mathrm{3}} =\alpha^{\mathrm{3}}…

can-we-find-the-black-area-the-shadow-of-earth-on-the-moon-during-moon-eclipse-after-time-t-of-its-starting-Given-Moon-radius-R-m-Earth-rafius-R-e-Sun-radius-R-s-e-and-m-given-both-anticlo

Question Number 226115 by fantastic2 last updated on 20/Nov/25 $${can}\:{we}\:{find}\:{the}\:{black}\:{area} \\ $$$$\left({the}\:{shadow}\:{of}\:{earth}\right){on}\:{the}\:{moon}\:{during} \\ $$$${moon}\:{eclipse}\:{after}\:{time}\:{t}\:{of} \\ $$$${its}\:{starting}? \\ $$$${Given}: \\ $$$${Moon}\:{radius}={R}_{{m}} \\ $$$${Earth}\:{rafius}={R}_{{e}} \\ $$$${Sun}\:{radius}={R}_{{s}} \\…

Show-that-the-equation-1-sin-cos-1-sin-cos-1-may-be-express-in-the-form-a-sin-2-bsin-c-0-where-a-b-and-c-are-constants-to-be-found-

Question Number 226111 by Linton last updated on 19/Nov/25 $${Show}\:{that}\:{the}\:{equation} \\ $$$$\frac{\mathrm{1}}{{sin}\theta+{cos}\theta}\:+\:\frac{\mathrm{1}}{{sin}\theta−{cos}\theta}\:=\:\mathrm{1} \\ $$$${may}\:{be}\:{express}\:{in}\:{the}\:{form} \\ $$$${a}\left({sin}\theta\right)^{\mathrm{2}} +{bsin}\theta+{c}=\mathrm{0}\:{where}\:{a}\:{b}\: \\ $$$${and}\:{c}\:{are}\:{constants}\:{to}\:{be}\:{found}. \\ $$ Answered by Frix last…

Question-226015

Question Number 226015 by mr W last updated on 18/Nov/25 Answered by fantastic2 last updated on 18/Nov/25 $${f}\left({x}\right)+{f}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}}\right)={x}…\left({i}\right) \\ $$$${put}\:{x}=\mathrm{2}\:{in}\:{i} \\ $$$${f}\left(\mathrm{2}\right)+{f}\left(−\mathrm{1}\right)=\mathrm{2}….\mathrm{1} \\ $$$${put}\:−\mathrm{1}\:{in}\:{i} \\…

The-coefficient-of-x-2-in-the-expansion-of-1-2-p-x-5-1-px-6-is-70-Find-the-possible-values-of-the-constant-p-

Question Number 226053 by Linton last updated on 18/Nov/25 $${The}\:{coefficient}\:{of}\:{x}^{\mathrm{2}} \:{in}\:{the}\:{expansion} \\ $$$${of}\:\left(\mathrm{1}+\:\left(\mathrm{2}/{p}\right){x}\right)^{\mathrm{5}} \:+\:\left(\mathrm{1}+{px}\right)^{\mathrm{6}} \:{is}\:\mathrm{70}. \\ $$$${Find}\:{the}\:{possible}\:{values}\:{of}\:{the} \\ $$$${constant}\:{p}. \\ $$ Answered by mr W…