Menu Close

Category: Arithmetic

Question-200972

Question Number 200972 by Mingma last updated on 27/Nov/23 Answered by AST last updated on 27/Nov/23 $${a}^{\mathrm{2}} ={b}^{\mathrm{2}} \left({b}+\mathrm{2}\right);{a}={b}\sqrt{{b}+\mathrm{2}} \\ $$$${b}=\left(\frac{{x}}{{y}}\right)^{\mathrm{2}} −\mathrm{2}\Rightarrow\left({a},{b}\right)=\left(\frac{{x}^{\mathrm{3}} −\mathrm{2}{xy}^{\mathrm{2}} }{{y}^{\mathrm{3}} },\frac{{x}^{\mathrm{2}}…

Question-200627

Question Number 200627 by cherokeesay last updated on 21/Nov/23 Answered by Frix last updated on 21/Nov/23 $$\mathrm{The}\:\mathrm{1}^{\mathrm{st}} \:\mathrm{equation}\:\mathrm{is}\:\mathrm{true}\:\mathrm{for}\:{y}=\frac{\mathrm{1}}{{x}} \\ $$$$\Rightarrow\:{x}=\mathrm{2}\wedge{y}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Commented by cherokeesay…

Question-200657

Question Number 200657 by cherokeesay last updated on 21/Nov/23 Answered by Frix last updated on 21/Nov/23 $$\mathrm{3}\sqrt[{\mathrm{4}}]{\mathrm{27}{x}^{\mathrm{2}} +\mathrm{24}{x}+\frac{\mathrm{28}}{\mathrm{3}}}=\mathrm{4}+\sqrt[{\mathrm{3}}]{\frac{\mathrm{81}{x}}{\mathrm{2}}−\mathrm{1}} \\ $$$$\mathrm{3}\sqrt[{\mathrm{4}}]{\frac{\mathrm{81}{x}^{\mathrm{2}} +\mathrm{72}{x}+\mathrm{28}}{\mathrm{3}}}=\mathrm{4}+\sqrt[{\mathrm{3}}]{\frac{\mathrm{81}{x}−\mathrm{2}}{\mathrm{2}}} \\ $$$${x}=\frac{{t}}{\mathrm{9}} \\ $$$$\mathrm{3}\sqrt[{\mathrm{4}}]{\frac{{t}^{\mathrm{2}}…

Question-200265

Question Number 200265 by cherokeesay last updated on 16/Nov/23 Answered by witcher3 last updated on 16/Nov/23 $$\begin{cases}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}\right)^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} −\mathrm{2}.\mathrm{5}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}\right)=\mathrm{0}}\\{\left(\mathrm{2}\right)\Leftrightarrow\left(\mathrm{2}\right)}\end{cases} \\ $$$$\Leftrightarrow\begin{cases}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}−\mathrm{5}\right)^{\mathrm{2}} =\mathrm{0}}\\{\sqrt{\left(\mathrm{x}^{\mathrm{2}}…