Question Number 223374 by behi834171 last updated on 22/Jul/25 Answered by Ghisom last updated on 22/Jul/25 $${r}^{\mathrm{4}} +\mathrm{4}{r}+\mathrm{1}=\mathrm{0} \\ $$$${r}^{\mathrm{4}} =−\mathrm{4}{r}−\mathrm{1} \\ $$$${r}^{\mathrm{4}} −\mathrm{1}=−\mathrm{4}{r}−\mathrm{2} \\…
Question Number 223354 by ajfour last updated on 22/Jul/25 Commented by ajfour last updated on 22/Jul/25 https://g.co/gemini/share/a41e606602a3 Commented by ajfour last updated on 22/Jul/25 Commented…
Question Number 223261 by Rojarani last updated on 19/Jul/25 Commented by Frix last updated on 20/Jul/25 $$\mathrm{We}\:\mathrm{cannot}\:\mathrm{solve}\:\mathrm{for}\:{p}\:\mathrm{and}\:{q}\:\mathrm{because}\:\mathrm{we}'\mathrm{ve} \\ $$$$\mathrm{got}\:\mathrm{only}\:\mathrm{1}\:\mathrm{equation}\:\mathrm{but}\:\mathrm{3}\:\mathrm{unknowns}\:{x},\:{p},\:{q} \\ $$$$\mathrm{if}\:{a},\:{b},\:{c},\:{d}\:\mathrm{are}\:\mathrm{given} \\ $$$$\mathrm{What}\:\mathrm{do}\:\mathrm{you}\:\mathrm{mean}?\:\mathrm{You}\:\mathrm{must}\:\mathrm{give}\:\mathrm{more} \\ $$$$\mathrm{information}.…
Question Number 223256 by ajfour last updated on 19/Jul/25 Commented by ajfour last updated on 19/Jul/25 Commented by ajfour last updated on 19/Jul/25 $$\:\: \\…
Question Number 223240 by fantastic last updated on 19/Jul/25 $${x}^{{x}} ={i} \\ $$$${number}\:{of}\:{solutions}?? \\ $$ Answered by mr W last updated on 19/Jul/25 $${say}\:{x}={re}^{\theta{i}} ={e}^{\mathrm{ln}\:{r}+\theta{i}}…
Question Number 223267 by behi834171 last updated on 19/Jul/25 $$\boldsymbol{{r}},\boldsymbol{{s}},\boldsymbol{{t}}\:;\:\boldsymbol{{are}}\:\boldsymbol{{the}}\:\boldsymbol{{roots}}\:\boldsymbol{{of}}: \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{{x}}^{\mathrm{3}} +\mathrm{5}\boldsymbol{{x}}+\mathrm{1}=\mathrm{0} \\ $$$$\boldsymbol{{find}}: \\ $$$$\:\:\:\:\:\:\left(\boldsymbol{{r}}^{\mathrm{3}} −\mathrm{1}\right)\left(\boldsymbol{{s}}^{\mathrm{3}} −\mathrm{1}\right)\left(\boldsymbol{{t}}^{\mathrm{3}} −\mathrm{1}\right) \\ $$ Answered by gregori…
Question Number 223230 by hardmath last updated on 18/Jul/25 $$\mathrm{Maksimum}\:\left(\frac{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}}\right)\:=\:? \\ $$ Answered by fantastic last updated on 18/Jul/25 $${Let}\:{f}\left({x}\right)=\left(\frac{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\right) \\…
Question Number 223216 by Ari last updated on 18/Jul/25 Answered by som(math1967) last updated on 18/Jul/25 $${let}\:{alcohol}=\mathrm{4}{xl},\:{water}=\mathrm{3}{xl} \\ $$$$\:\therefore\:\frac{\mathrm{4}{x}}{\mathrm{3}{x}+\mathrm{7}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\Rightarrow\mathrm{16}{x}=\mathrm{9}{x}+\mathrm{21} \\ $$$$\Rightarrow\mathrm{7}{x}=\mathrm{21}\Rightarrow{x}=\mathrm{3} \\ $$$$\:{amount}\:{of}\:{alcohol}=\mathrm{4}×\mathrm{3}=\mathrm{12}{l}…
Question Number 223203 by ajfour last updated on 17/Jul/25 $${Find}\:{x}\:{and}\:{y} \\ $$$$\:\:\:\:{ix}+{y}={ix}^{\mathrm{3}} −{y}^{\mathrm{3}} \\ $$$$\:\:\:{and}\: \\ $$$$\:\:\:\:{xy}\left({y}−{ix}\right)={c} \\ $$ Answered by mr W last updated…
Question Number 223161 by Rojarani last updated on 16/Jul/25 $${Solve}\:{for}\:{x}\:{if} \\ $$$$\:\sqrt{{x}+\mathrm{1}}+\sqrt{{x}−\mathrm{1}}=\mathrm{1} \\ $$ Commented by fantastic last updated on 16/Jul/25 $${Why}\:{am}\:{i}\:{getting}\:\frac{\mathrm{5}}{\mathrm{4}}?? \\ $$ Commented…