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Category: Algebra

Find-3-2-5-1-4-3-2-5-1-4-1-4-5-1-4-1-5-1-4-1-

Question Number 225323 by hardmath last updated on 21/Oct/25 $$\mathrm{Find}:\:\:\:\left(\frac{\mathrm{3}\:+\:\mathrm{2}\:\sqrt[{\mathrm{4}}]{\mathrm{5}}}{\mathrm{3}\:-\:\mathrm{2}\:\sqrt[{\mathrm{4}}]{\mathrm{5}}}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} .\:\:\:\frac{\sqrt[{\mathrm{4}}]{\mathrm{5}}\:-\:\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{\mathrm{5}}\:+\:\mathrm{1}}\:\:=\:? \\ $$ Answered by Raphael254 last updated on 21/Oct/25 $$ \\ $$$$\sqrt[{\mathrm{4}}]{\frac{\mathrm{3}+\mathrm{2}\sqrt[{\mathrm{4}}]{\mathrm{5}}}{\mathrm{3}−\mathrm{2}\sqrt[{\mathrm{4}}]{\mathrm{5}}}}×\sqrt[{\mathrm{4}}]{\frac{\mathrm{6}\sqrt{\mathrm{5}}\:+\:\mathrm{6}\:−\:\mathrm{4}\sqrt[{\mathrm{4}}]{\mathrm{125}}\:−\:\mathrm{4}\sqrt[{\mathrm{4}}]{\mathrm{5}}}{\mathrm{6}\sqrt{\mathrm{5}}\:+\:\mathrm{6}\:+\:\mathrm{4}\sqrt[{\mathrm{4}}]{\mathrm{125}}\:+\:\mathrm{4}\sqrt[{\mathrm{4}}]{\mathrm{5}}}} \\ $$$$…

if-fogoh-x-cos-2-x-9-then-f-x-g-x-h-x-

Question Number 225330 by mathlove last updated on 21/Oct/25 $${if}\:\:\left({fogoh}\right)\left({x}\right)={cos}^{\mathrm{2}} \left({x}+\mathrm{9}\right) \\ $$$${then}\:\:\:{f}\left({x}\right)=?\:,\:\:{g}\left({x}\right)=?\:\:,\:{h}\left({x}\right)=? \\ $$ Answered by Raphael254 last updated on 21/Oct/25 $$ \\ $$$${f}\left({g}\left({h}\left({x}\right)\right)\right)\:=\:{cos}^{\mathrm{2}}…

Question-225241

Question Number 225241 by Spillover last updated on 18/Oct/25 Answered by som(math1967) last updated on 19/Oct/25 $$\:{tan}\theta=\frac{{nsin}\alpha{cos}\alpha.{sec}^{\mathrm{2}} \alpha}{\left(\mathrm{1}−{nsin}^{\mathrm{2}} \alpha\right){sec}^{\mathrm{2}} \alpha} \\ $$$$\Rightarrow{tan}\theta=\frac{{ntan}\alpha}{{sec}^{\mathrm{2}} \alpha−{ntan}^{\mathrm{2}} \alpha} \\…

Question-225240

Question Number 225240 by Spillover last updated on 18/Oct/25 Answered by mr W last updated on 19/Oct/25 $$\left({a}\right) \\ $$$${R}=\frac{\mid\mathrm{3}×\mathrm{5}−\mathrm{4}×\mathrm{4}+\mathrm{6}\mid}{\:\sqrt{\mathrm{3}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} }}=\mathrm{1} \\ $$$$\Rightarrow\left({x}−\mathrm{5}\right)^{\mathrm{2}} +\left({y}−\mathrm{4}\right)^{\mathrm{2}}…

Question-225098

Question Number 225098 by Ark55 last updated on 17/Oct/25 Answered by Rasheed.Sindhi last updated on 17/Oct/25 $$\mathrm{5}{x}+\frac{\mathrm{1}}{{x}}=\mathrm{6} \\ $$$$\left(\mathrm{5}{x}+\frac{\mathrm{1}}{{x}}=\mathrm{6}\right)^{\mathrm{2}} \\ $$$$\mathrm{25}{x}^{\mathrm{2}} +\mathrm{10}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }=\mathrm{36} \\ $$$$\mathrm{25}{x}^{\mathrm{2}}…