Category: Algebra

Question Number 22244 by ajfour last updated on 14/Oct/17 $$Solvetheinequality:$$$$-9\left(\sqrt[4]{x}\right)+\sqrt{x}+18⩾0.$$ Answered by $@ty@mlastupdatedon14/Oct/17$$Let\sqrt{x}=y$$$$−\mathrm{9}\sqrt{{y}}+{y}+\mathrm{18}\geqslant\mathrm{0} \…

Question Number 87755 by john santu last updated on 06/Apr/20 $$\mathrm{f}\left(\frac{\mathrm{x}-3}{\mathrm{x}+1}\right)+\mathrm{f}\left(\frac{\mathrm{x}+3}{1-\mathrm{x}}\right)=\mathrm{x}$$$$\mathrm{find}\mathrm{f}\left(\mathrm{x}\right)$$ Commented by john santu last updated on 06/Apr/20 $$\left(\mathrm{i}\right)\:\mathrm{let}\:\frac{\mathrm{x}−\mathrm{3}}{\mathrm{x}+\mathrm{1}}\:=\:\mathrm{x}'\:\Rightarrow\mathrm{f}\left(\mathrm{x}'\right)\:+\:\mathrm{f}\left(\frac{\mathrm{x}'−\mathrm{3}}{\mathrm{x}'+\mathrm{1}}\right)\:=\:\frac{\mathrm{x}'+\mathrm{3}}{\mathrm{1}−\mathrm{x}} \…

Question Number 87737 by M±th+et£s last updated on 05/Apr/20 $$solve$$$$sin\left(\frac{\pi }{\left[\frac{\left[x\right]}{4}\right]}\right)=\frac{1}{2}$$ Answered by mahdi last updated on 06/Apr/20 $$\mathrm{u}=\left[\frac{\left[\mathrm{x}\right]}{4}\right]\Rightarrow -1⩽\frac{1}{\mathrm{u}}⩽1\Rightarrow -\pi ⩽\frac{\pi }{\mathrm{u}}⩽\pi \{\mathrm{u}\ne 0\Rightarrow \mathrm{x}\notin [0,4)\}$$$$\mathrm{sin}\left(\frac{\pi}{\mathrm{u}}\right)=\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow$$\{\begin{array}{l}\frac{\pi }{\mathrm{u}}=\frac{\pi }{6}+2\mathrm{k}\pi \\ \frac{\pi }{\mathrm{u}}=\frac{5\pi }{6}+2\mathrm{k}\pi \end{array}$$ \…

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Question Number 153263 by mnjuly1970 last updated on 06/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com