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Category: Algebra

let-be-a-root-of-the-equation-x-4-x-1-4-1-0-find-300-301-

Question Number 158124 by HongKing last updated on 31/Oct/21 $$\mathrm{let}\:\boldsymbol{\omega}\:\mathrm{be}\:\mathrm{a}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{x}^{\mathrm{4}} \:+\:\left(\mathrm{x}\:-\:\mathrm{1}\right)^{\mathrm{4}} \:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{find}\:\:\boldsymbol{\Omega}\:=\:\boldsymbol{\omega}^{\mathrm{300}} \:+\:\boldsymbol{\omega}^{\mathrm{301}} \\ $$ Answered by Rasheed.Sindhi last updated on…

Considering-y-x-3-px-q-If-dy-dx-x-0-2-p-3-if-d-y-x-dx-x-0-3-q-2-roots-of-the-cubic-eq-n-are-x-3-6-6-1-3-

Question Number 27046 by ajfour last updated on 01/Jan/18 $${Considering}\:\boldsymbol{{y}}=\boldsymbol{{x}}^{\mathrm{3}} +\boldsymbol{{px}}+\boldsymbol{{q}} \\ $$$${If}\:\:\:\:\:\frac{{dy}}{{dx}}\mid_{{x}=\alpha} =\mathrm{0}\:\:\Rightarrow\:\:\alpha^{\mathrm{2}} =−\frac{{p}}{\mathrm{3}} \\ $$$${if}\:\:\:\frac{{d}\left({y}/{x}\right)}{{dx}}\mid_{{x}=\beta} =\mathrm{0}\:\:\:\Rightarrow\:\beta^{\:\mathrm{3}} =\frac{{q}}{\mathrm{2}} \\ $$$${roots}\:{of}\:{the}\:{cubic}\:\:{eq}^{{n}} \:{are}: \\ $$$$\:\:\:\:{x}=\left[−\beta^{\:\mathrm{3}} \pm\sqrt{\beta^{\:\mathrm{6}}…

Posting-Question-with-Images-Preferably-you-should-type-the-question-However-if-you-are-using-pictures-then-please-do-the-following-steps-which-posting-a-photo-of-printed-question-A-Use-camscanner-

Question Number 92566 by Tinku Tara last updated on 08/May/20 $$\mathrm{Posting}\:\mathrm{Question}\:\mathrm{with}\:\mathrm{Images} \\ $$$$\mathrm{Preferably}\:\mathrm{you}\:\mathrm{should}\:\mathrm{type}\:\mathrm{the}\:\mathrm{question}. \\ $$$$\mathrm{However}\:\mathrm{if}\:\mathrm{you}\:\mathrm{are}\:\mathrm{using}\:\mathrm{pictures}\:\mathrm{then} \\ $$$$\mathrm{please}\:\mathrm{do}\:\mathrm{the}\:\mathrm{following}\:\mathrm{steps} \\ $$$$\mathrm{which}\:\mathrm{posting}\:\mathrm{a}\:\mathrm{photo}\:\mathrm{of}\:\mathrm{printed} \\ $$$$\mathrm{question}. \\ $$$$\mathrm{A}.\:\mathrm{Use}\:\mathrm{camscanner}\:\mathrm{app}\:\mathrm{to}\:\mathrm{take}\: \\ $$$$\mathrm{pictures}\:\left(\mathrm{search}\:\mathrm{for}\:\mathrm{camscanner}\:\mathrm{in}\right.…

Question-158097

Question Number 158097 by zainaltanjung last updated on 31/Oct/21 Answered by Rasheed.Sindhi last updated on 31/Oct/21 $${x}^{\mathrm{2}} +{px}+\mathrm{12}:{Roots}\:\alpha\:,\:\mathrm{4} \\ $$$$\mathrm{product}\:{of}\:{roots}:\mathrm{4}\alpha=\mathrm{12}\Rightarrow\alpha=\mathrm{3}\:\left({other}\:{root}\right) \\ $$$${sum}\:{of}\:{roots}:\mathrm{4}+\mathrm{3}=−\mathrm{p}\Rightarrow\mathrm{p}=−\mathrm{7} \\ $$$${x}^{\mathrm{2}} +{px}+{q}=\mathrm{0}\Rightarrow{x}^{\mathrm{2}}…

The-result-of-5-8-2-3-6-2-is-

Question Number 158098 by zainaltanjung last updated on 31/Oct/21 $$\: \\ $$$$\mathrm{The}\:\mathrm{result}\:\mathrm{of}: \\ $$$$\:\left[\mathrm{5}\:+\:\left\{\left(\mathrm{8}\right)\:×\:\left(−\:\:\mathrm{2}\right)\right\}\right]\:+\mathrm{3}\left\{\mathrm{6}\:+\:\left(\:\:\mathrm{2}\right)\right\}\:\mathrm{is}\:.\:.\: \\ $$ Commented by Rasheed.Sindhi last updated on 31/Oct/21 $${I}\:{think},\:{the}\:{forum}\:{is}\:{not}\:{for}\:{primary} \\…

If-a-1-5-a-2-13-and-a-n-2-5a-n-1-6a-n-Find-a-n-

Question Number 92557 by I want to learn more last updated on 07/May/20 $$\mathrm{If}\:\:\:\mathrm{a}_{\mathrm{1}} \:\:=\:\:\mathrm{5},\:\:\:\:\:\mathrm{a}_{\mathrm{2}} \:\:=\:\:\mathrm{13}\:\:\:\:\:\mathrm{and}\:\:\:\:\mathrm{a}_{\mathrm{n}\:\:+\:\:\mathrm{2}} \:\:\:=\:\:\mathrm{5a}_{\mathrm{n}\:\:+\:\:\mathrm{1}} \:−\:\:\mathrm{6a}_{\mathrm{n}} . \\ $$$$\mathrm{Find}\:\:\:\:\:\mathrm{a}_{\mathrm{n}} \\ $$ Commented by…