Question Number 179195 by mathlove last updated on 26/Oct/22 $${a}+\frac{\mathrm{1}}{{b}}={tan}\mathrm{59} \\ $$$${b}+\frac{\mathrm{1}}{{c}}={tan}\mathrm{60} \\ $$$${c}+\frac{\mathrm{1}}{{a}}={tan}\mathrm{61} \\ $$$$\left({abc}\right)^{\mathrm{2022}} +\frac{\mathrm{1}}{\left({abc}\right)^{\mathrm{2022}} }=? \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 179157 by Agnibhoo98 last updated on 25/Oct/22 $$\mathrm{If}\:{x}\:=\:{a}^{\mathrm{2}} −\:{bc},\:{y}\:=\:{b}^{\mathrm{2}} \:−\:{ca},\:{z}\:=\:{c}^{\mathrm{2}} \:−\:{ab} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}, \\ $$$${x}^{\mathrm{3}} \:+\:{y}^{\mathrm{3}} \:+\:{z}^{\mathrm{3}} \:−\:\mathrm{3}{xyz}\:\mathrm{is}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}. \\ $$ Answered by som(math1967)…
Question Number 179140 by Shrinava last updated on 25/Oct/22 $$\frac{\mathrm{1}}{\mathrm{3a}}\:=\:\frac{\mathrm{1}}{\mathrm{4b}}\:=\:\frac{\mathrm{1}}{\mathrm{6c}}\:\:\:\mathrm{and}\:\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{27} \\ $$$$\mathrm{find}\:\:\:\mathrm{a}−\mathrm{c}=? \\ $$ Answered by Frix last updated on 25/Oct/22 $${a}=\mathrm{4}{t} \\ $$$${b}=\mathrm{3}{t} \\…
Question Number 48075 by MJS last updated on 19/Nov/18 $$\mathrm{solve}\:\:\:\:\:\left(\mid{x}^{\mathrm{2}} −\mathrm{1}\mid−\frac{\mathrm{1}}{\mathrm{2}}\right){x}+\frac{\sqrt{\mathrm{6}}}{\mathrm{18}}=\mathrm{0} \\ $$ Commented by MJS last updated on 19/Nov/18 $$\mathrm{case}\:\mathrm{1} \\ $$$${x}<−\mathrm{1} \\ $$$${x}^{\mathrm{3}}…
Question Number 48055 by F_Nongue last updated on 21/Nov/18 $${Solve}\:{the}\:{system}: \\ $$$$\begin{cases}{{x}^{\mathrm{3}} +{x}^{\mathrm{2}} {y}−\mathrm{4}{xy}^{\mathrm{2}} −\mathrm{4}{y}^{\mathrm{3}} =\mathrm{0}}\\{{x}^{\mathrm{2}} −\mathrm{2}{xy}−\mathrm{3}{y}^{\mathrm{2}} −{x}−{y}=\mathrm{0}}\end{cases} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated…
Question Number 179105 by Shrinava last updated on 24/Oct/22 $$\mathrm{1}.\:\mathrm{Compare}:\:\:\:\pi^{\mathrm{2022}\boldsymbol{\mathrm{e}}} \:\:\:\mathrm{and}\:\:\:\mathrm{e}^{\mathrm{2022}\boldsymbol{\pi}} \\ $$$$\mathrm{2}.\:\mathrm{Compute}\:\mathrm{value}\:\mathrm{of}\:\:\:\mathrm{P}\:=\:\pi^{\boldsymbol{\pi}^{\boldsymbol{\pi}^{…^{\boldsymbol{\pi}} } } } \\ $$ Answered by MJS_new last updated on 25/Oct/22…
Question Number 179100 by mr W last updated on 24/Oct/22 $${if}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{xy}=\mathrm{5},\:{find}\:{the}\:{range}\:{of} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −{xy}. \\ $$$$\left({x},{y}\:\in\mathbb{R}\right) \\ $$ Commented by Frix last…
Question Number 179095 by SAMIRA last updated on 24/Oct/22 Commented by HeferH last updated on 24/Oct/22 $${x}_{\mathrm{1}} =\mathrm{1};\:{x}_{\mathrm{2}} =\mathrm{0}\: \\ $$$$\: \\ $$ Answered by…
Question Number 179090 by CrispyXYZ last updated on 24/Oct/22 $$\mathrm{Given}\:{a}>\mathrm{0},\:{b}>\mathrm{0},\:{c}>\mathrm{2},\:{a}+{b}=\mathrm{1}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\:\frac{\mathrm{3}{ac}}{{b}}+\frac{{c}}{{ab}}+\frac{\mathrm{6}}{{c}−\mathrm{2}}. \\ $$ Commented by Frix last updated on 24/Oct/22 $$\mathrm{24} \\ $$ Answered…
Question Number 179064 by HeferH last updated on 24/Oct/22 Commented by HeferH last updated on 24/Oct/22 $${is}\:{this}\:{correct}? \\ $$ Commented by Rasheed.Sindhi last updated on…