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Category: Algebra

Question-113885

Question Number 113885 by Aina Samuel Temidayo last updated on 16/Sep/20 Answered by MJS_new last updated on 16/Sep/20 $${x}=\frac{\mathrm{ln}\:{bc}}{\mathrm{ln}\:{a}}\:\:\:\:\:{y}=\frac{\mathrm{ln}\:{ac}}{\mathrm{ln}\:{b}}\:\:\:\:\:{z}=\frac{\mathrm{ln}\:{ab}}{\mathrm{ln}\:{c}} \\ $$$$\mathrm{ln}\:{a}\:={o};\:\mathrm{ln}\:{b}\:={p}\:;\:\mathrm{ln}\:{c}\:={q} \\ $$$${xyz}=\frac{{o}}{{p}}+\frac{{o}}{{q}}+\frac{{p}}{{o}}+\frac{{p}}{{q}}+\frac{{q}}{{o}}+\frac{{q}}{{p}}+\mathrm{2}={x}+{y}+{z}+\mathrm{2} \\ $$…

find-the-values-of-k-for-which-the-line-y-kx-3-does-not-meet-the-curve-y-2x-2-3x-k-

Question Number 113857 by ayenisamuel last updated on 15/Sep/20 $${find}\:{the}\:{values}\:{of}\:{k}\:{for}\:{which}\:{the} \\ $$$${line}\:{y}={kx}−\mathrm{3}\:{does}\:{not}\:{meet}\:{the}\:{curve} \\ $$$${y}=\mathrm{2}{x}^{\mathrm{2}} −\mathrm{3}{x}+{k}. \\ $$ Answered by MJS_new last updated on 15/Sep/20 $$\mathrm{first},\:\mathrm{intersect}\:\mathrm{them}…

if-f-x-2x-2-12x-10-i-sketch-the-graph-of-y-f-x-for-1-x-7-ii-find-the-set-of-values-of-k-for-which-the-equation-f-x-k-has-4-distinct-roots-

Question Number 113854 by ayenisamuel last updated on 15/Sep/20 $${if}\:{f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{2}} −\mathrm{12}{x}+\mathrm{10}.\: \\ $$$$\left({i}\right)\:{sketch}\:{the}\:{graph}\:{of}\:{y}=\mid{f}\left({x}\right)\mid\:{for} \\ $$$$−\mathrm{1}\leqslant{x}\leqslant\mathrm{7}. \\ $$$$\left({ii}\right)\:{find}\:{the}\:{set}\:{of}\:{values}\:{of}\:{k}\:{for} \\ $$$${which}\:{the}\:{equation}\:\mid{f}\left({x}\right)\mid={k}\:{has}\:\mathrm{4} \\ $$$${distinct}\:{roots}. \\ $$ Answered by…

x-2-4x-1-9-

Question Number 48306 by Messias last updated on 21/Nov/18 $$\mathrm{x}^{\mathrm{2}} +\mathrm{4x}+\mathrm{1}=\mathrm{9} \\ $$ Answered by MJS last updated on 21/Nov/18 $${x}^{\mathrm{2}} +{px}+{q}=\mathrm{0}\:\Rightarrow\:{x}=−\frac{{p}}{\mathrm{2}}\pm\sqrt{\frac{{p}^{\mathrm{2}} }{\mathrm{4}}−{q}} \\ $$$$\mathrm{in}\:\mathrm{this}\:\mathrm{case}:\:{p}=\mathrm{4};\:{q}=−\mathrm{8}…

Question-48294

Question Number 48294 by behi83417@gmail.com last updated on 21/Nov/18 Commented by MJS last updated on 22/Nov/18 $${x}^{\mathrm{6}} +{x}^{\mathrm{5}} +{x}^{\mathrm{4}} −\mathrm{10}{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +{x}+\mathrm{1}=\mathrm{0} \\ $$$${x}=\mathrm{tan}\:\frac{{t}}{\mathrm{2}} \\…