Question Number 217958 by dscm last updated on 23/Mar/25 $${a},{b},{c}\in\mathbb{Z}^{+} {and} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{ab}+{bc}+{ca}=\mathrm{2025} \\ $$$${find}\:{out}\:{all}\:{triplets}\:\left({a},{b},{c}\right). \\ $$ Commented by Unhombre last updated…
Question Number 217894 by hardmath last updated on 23/Mar/25 $$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{holds}: \\ $$$$\Sigma\:\frac{\mathrm{cot}\:\mathrm{A}}{\:\sqrt{\mathrm{cot}\:\mathrm{B}\:\:+\:\:\mathrm{3}\:\mathrm{cot}\:\mathrm{C}}}\:\:\geqslant\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\:\sqrt[{\mathrm{4}}]{\mathrm{27}}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 217895 by hardmath last updated on 23/Mar/25 Commented by mr W last updated on 23/Mar/25 $${question}\:{is}\:{wrong}.\:{C}_{{n}} ^{{r}} \:{is}\:{only}\:{defined} \\ $$$${for}\:\mathrm{0}\leqslant{r}\leqslant{n}. \\ $$ Commented…
Question Number 217952 by dscm last updated on 23/Mar/25 $${If}\:{x}\in\mathbb{Z}\:\wedge{y}\:{non}-{negative}\:{integer} \\ $$$${such}\:{that} \\ $$$${x}^{\mathrm{2}} +\mathrm{10}{x}+\mathrm{23}=\mathrm{2}^{{y}} \\ $$$${find}\:{out}\:{x},{y} \\ $$ Answered by Frix last updated on…
Question Number 217888 by ArshadS last updated on 23/Mar/25 $${Solve}: \\ $$$$\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{15}}=\frac{{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{6}}{{x}^{\mathrm{2}} −\mathrm{10}{x}+\mathrm{24}} \\ $$ Answered by bagjahebat last updated on 23/Mar/25…
Question Number 217949 by hardmath last updated on 23/Mar/25 Commented by hardmath last updated on 23/Mar/25 $$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} \:=\:? \\ $$ Answered by A5T…
Question Number 217887 by ArshadS last updated on 23/Mar/25 $${Solve}\:: \\ $$$$\frac{{x}+\mathrm{1}}{{x}−\mathrm{2}}+\frac{{x}−\mathrm{1}}{{x}+\mathrm{2}}=\frac{\mathrm{2}{x}+\mathrm{1}}{{x}−\mathrm{1}}+\frac{\mathrm{2}{x}−\mathrm{1}}{{x}+\mathrm{1}} \\ $$ Answered by Rasheed.Sindhi last updated on 23/Mar/25 $$\frac{{x}+\mathrm{1}}{{x}−\mathrm{2}}−\mathrm{1}+\frac{{x}−\mathrm{1}}{{x}+\mathrm{2}}−\mathrm{1}+\mathrm{2}=\frac{\mathrm{2}{x}+\mathrm{1}}{{x}−\mathrm{1}}−\mathrm{2}+\frac{\mathrm{2}{x}−\mathrm{1}}{{x}+\mathrm{1}}−\mathrm{2}+\mathrm{4} \\ $$$$\frac{\mathrm{3}}{{x}−\mathrm{2}}+\frac{−\mathrm{3}}{{x}+\mathrm{2}}=\frac{\mathrm{3}}{{x}−\mathrm{1}}+\frac{−\mathrm{3}}{{x}+\mathrm{1}}+\mathrm{2} \\…
Question Number 217881 by OmoloyeMichael last updated on 23/Mar/25 Answered by vnm last updated on 23/Mar/25 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} {x}\left(\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} {x}}+\frac{\mathrm{cos}\:{x}}{\mathrm{1}+\mathrm{sin}^{\mathrm{2}} {x}}\right){dx}={I} \\ $$$${f}\left({x}\right)=\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} {x}}+\frac{\mathrm{cos}\:{x}}{\mathrm{1}+\mathrm{sin}^{\mathrm{2}} {x}}…
Question Number 217940 by ArshadS last updated on 23/Mar/25 $${Solve} \\ $$$$\sqrt{\mathrm{2}{x}+\mathrm{7}}\:\:−\sqrt{{x}−\mathrm{1}}\:=\mathrm{2}\:\:\:\:\:\:\:\:\:\:\: \\ $$ Answered by Frix last updated on 23/Mar/25 $$\mathrm{No}\:\mathrm{real}\:\mathrm{solution}\:\mathrm{because}\:\mathrm{min}\:\left(\mathrm{lhs}\right)\:>\mathrm{2} \\ $$$${a},\:{b}\:\in\mathbb{R}\wedge{b}\neq\mathrm{0} \\…
Question Number 217937 by Tawa11 last updated on 23/Mar/25 Commented by Tawa11 last updated on 23/Mar/25 $$\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{other}\:\mathrm{possible}\:\mathrm{answer}? \\ $$ Commented by Tawa11 last updated on…