Question Number 224018 by hardmath last updated on 14/Aug/25 $$\mathrm{x}\:\neq\:\mathrm{y} \\ $$$$\lambda\:\geqslant\:\mathrm{1} \\ $$$$\begin{cases}{\mathrm{x}\:+\:\lambda^{\mathrm{2}} \:=\:\left(\mathrm{y}\:−\:\lambda\right)^{\mathrm{2}} }\\{\mathrm{y}\:+\:\lambda^{\mathrm{2}} \:=\:\left(\mathrm{x}\:−\:\lambda\right)^{\mathrm{2}} }\end{cases} \\ $$$$\mathrm{Find}:\:\:\:\left(\frac{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} }{\mathrm{4}\lambda^{\mathrm{2}} \:−\:\mathrm{1}}\right)^{\mathrm{2025}} =\:\:? \\…
Question Number 223995 by Rojarani last updated on 13/Aug/25 Answered by Frix last updated on 13/Aug/25 $$\mathrm{Let}\:{y}={px}\wedge{z}={qx},\:\mathrm{solve}\:\mathrm{for}\:{x}^{−\mathrm{2}} \\ $$$$\Rightarrow \\ $$$${x}^{−\mathrm{2}} =\begin{cases}{\mathrm{7}{p}^{\mathrm{2}} +\mathrm{9}{pq}+\mathrm{3}{q}^{\mathrm{2}} +\mathrm{13}{p}+\mathrm{9}{q}+\mathrm{7}}\\{\left(\mathrm{7}{p}^{\mathrm{2}} +\mathrm{13}{pq}+\mathrm{7}{q}^{\mathrm{2}}…
Question Number 224003 by mr W last updated on 13/Aug/25 Commented by mr W last updated on 13/Aug/25 $${the}\:{areas}\:{of}\:{two}\:{equilaterals}\:{are} \\ $$$${known}.\:{find}\:{the}\:{area}\:{of}\:{the}\:{third} \\ $$$${triangle}. \\ $$…
Question Number 223978 by fantastic last updated on 12/Aug/25 $${Guys}\:{my}\:{exams}\:{are}\:{starting} \\ $$$${from}\:{today}.{Wish}\:{me}\:{luck}! \\ $$ Commented by som(math1967) last updated on 12/Aug/25 $$\boldsymbol{{Best}}\:\boldsymbol{{of}}\:\:\boldsymbol{{luck}}\: \\ $$ Commented…
Question Number 223988 by MirHasibulHossain last updated on 12/Aug/25 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{DE}\:\mathrm{using}\:\mathrm{the}\:\mathrm{method}\:\mathrm{of}\:\mathrm{Frobenius}\::\: \\ $$$$\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\mathrm{y}''−\mathrm{2xy}'+\mathrm{n}\left(\mathrm{n}+\mathrm{1}\right)\mathrm{y}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 223990 by RoseAli last updated on 12/Aug/25 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{x}\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{5}} −\mathrm{32}\:}{{x}−\mathrm{1}} \\ $$ Commented by prathita last updated on 12/Aug/25 $$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}} \\ $$…
Question Number 223964 by Rojarani last updated on 11/Aug/25 Answered by Rasheed.Sindhi last updated on 11/Aug/25 $${x}^{\mathrm{3}} +\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{4}=\mathrm{0} \\ $$$${a},{b},{c}\:{are}\:{the}\:{roots} \\ $$$${a}+{b}+{c}=−\mathrm{2} \\ $$$${ab}+{bc}+{ca}=\mathrm{3}…
Question Number 223965 by Rojarani last updated on 11/Aug/25 Answered by Frix last updated on 11/Aug/25 $${z}={x}+{y}−\mathrm{7} \\ $$$$\mathrm{Insert}\:\mathrm{in}\:\left(\mathrm{2}\right)\:\Rightarrow\:{y}=\frac{\mathrm{7}{x}−\mathrm{43}}{{x}−\mathrm{7}} \\ $$$$\mathrm{Insert}\:\mathrm{in}\:\left(\mathrm{3}\right)\:\Rightarrow\:{x}^{\mathrm{2}} −\mathrm{19}{x}+\mathrm{90}=\mathrm{0} \\ $$$$\Rightarrow \\…
Question Number 223962 by behi834171 last updated on 11/Aug/25 Commented by behi834171 last updated on 11/Aug/25 $$\boldsymbol{{Area}}\:\boldsymbol{{of}}\:\boldsymbol{{circles}}: \\ $$$$\begin{cases}{\boldsymbol{{yellow}}=\mathrm{1}}\\{\boldsymbol{{blue}}=\sqrt{\mathrm{2}}}\\{\boldsymbol{{green}}=\sqrt{\mathrm{3}}}\end{cases}\:\:\:\:\:\:\left(\boldsymbol{{any}}\:\boldsymbol{{unit}}\right)^{\mathrm{2}} \\ $$$$\boldsymbol{{Area}}\:\boldsymbol{{of}}\:\boldsymbol{{gray}}\left(\boldsymbol{{big}}\right)\:\:\boldsymbol{{circle}}=? \\ $$$$ \\ $$$$\boldsymbol{{circles}}\:\boldsymbol{{and}}\:\boldsymbol{{lines}}\:\boldsymbol{{are}}\:\boldsymbol{{tangent}}\:\boldsymbol{{to}}…
Question Number 223958 by Nicholas666 last updated on 11/Aug/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{{x}\:\mathrm{sinh}\left({x}\right)}{\mathrm{1}+\mathrm{cosh}^{\mathrm{2}} \left({x}\right)}\:\mathrm{d}{x} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…