Question Number 154267 by mathdanisur last updated on 16/Sep/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\mathrm{and}\:\mathrm{xy}+\mathrm{yz}+\mathrm{zx}=\mathrm{3xyz}\:\:\mathrm{then}: \\ $$$$\left(\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{1}}{\mathrm{x}+\mathrm{y}}\right)\left(\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{1}}{\mathrm{2x}+\mathrm{y}+\mathrm{z}}\right)\:\leqslant\:\frac{\mathrm{9}}{\mathrm{8}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 154262 by mathlove last updated on 16/Sep/21 Answered by som(math1967) last updated on 16/Sep/21 $${lntan}\left(\frac{\pi}{\mathrm{180}}\right)+{lntan}\left(\frac{\mathrm{2}\pi}{\mathrm{180}}\right)+…{lntan}\left(\frac{\mathrm{89}\pi}{\mathrm{180}}\right) \\ $$$${lntan}\mathrm{1}°+{lntan}\mathrm{2}°+…{lntan}\mathrm{89}°\bigstar \\ $$$${lntan}\mathrm{1}×{tan}\mathrm{2}×…{tan}\mathrm{89} \\ $$$${lntan}\mathrm{1}×{cot}\left(\mathrm{90}−\mathrm{89}\right)×{tan}\mathrm{2}×{cot}\left(\mathrm{90}−\mathrm{88}\right)…×{tan}\mathrm{45} \\ $$$${lntan}\mathrm{1}×{cot}\mathrm{1}×{tan}\mathrm{2}×{cot}\mathrm{2}×…×\mathrm{1}…
Question Number 154258 by liberty last updated on 16/Sep/21 Answered by som(math1967) last updated on 16/Sep/21 $$\frac{{a}}{{b}+{c}}\:+\mathrm{1}+\frac{{b}}{{c}+{a}}+\mathrm{1}+\frac{{c}}{{a}+{b}}+\mathrm{1}=\mathrm{76}+\mathrm{3} \\ $$$$\:{or}\:\frac{{a}+{b}+{c}}{{b}+{c}}\:+\frac{{a}+{b}+{c}}{{c}+{a}}\:+\frac{{a}+{b}+{c}}{{a}+{b}}=\mathrm{79} \\ $$$${or}.\:\left({a}+{b}+{c}\right)\left(\frac{\mathrm{1}}{{b}+{c}}+\frac{\mathrm{1}}{{c}+{a}}+\frac{\mathrm{1}}{{a}+{b}}\right)=\mathrm{79} \\ $$$$\therefore\left(\frac{\mathrm{1}}{{a}+{b}}\:+\frac{\mathrm{1}}{{b}+{c}}+\frac{\mathrm{1}}{{c}+{a}}\right)=\frac{\mathrm{79}}{\mathrm{1580}}=\frac{\mathrm{1}}{\mathrm{20}}\bigstar \\ $$$$\bigstar{a}+{b}+{c}=\mathrm{1580}…
Question Number 88678 by Cheyboy last updated on 12/Apr/20 $$\boldsymbol{\mathrm{F}}{ind}\:\:\:\sqrt{\boldsymbol{{i}}}+\sqrt{−\boldsymbol{\mathrm{i}}} \\ $$ Commented by mr W last updated on 12/Apr/20 $${both}\:{definitions}\:{are}\:{used}\:\left({in}\:{different}\right. \\ $$$$\left.{countries}\right): \\ $$$$−\pi<{Arg}\left({z}\right)\leqslant\pi\:{or}…
Question Number 154204 by mathdanisur last updated on 15/Sep/21 Commented by Rasheed.Sindhi last updated on 16/Sep/21 $$\boldsymbol{\mathrm{Sorry}}\:\mathrm{that}\:\mathrm{I}\:\mathrm{neglect}\:“\:\frac{\mathrm{tan}\alpha\:}{\mathrm{tan}\beta\:}\:\in\mathbb{Z}^{+} \:''. \\ $$$$\mathrm{Now}\:\mathrm{the}\:\mathrm{question}\:\mathrm{can}\:\mathrm{be}\:\mathrm{solved}\:\mathrm{for} \\ $$$$\mathrm{some}\:\mathrm{fixed}\:\mathrm{answers}. \\ $$ Answered…
Question Number 154200 by amin96 last updated on 15/Sep/21 $${g}\left(\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\right)=\frac{\mathrm{7}{x}+\mathrm{3}}{{x}+\mathrm{1}}\:\:{and}\:\:{f}\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{3}\right)=\mathrm{3}{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{7} \\ $$$${find}\:\:\left({f}+{g}\right)\left({x}\right)=?\:\:\: \\ $$ Answered by Rasheed.Sindhi last updated on 15/Sep/21 $${g}\left(\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\right)=\frac{\mathrm{7}{x}+\mathrm{3}}{{x}+\mathrm{1}}\:\:{and}\:\:{f}\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{3}\right)=\mathrm{3}{x}^{\mathrm{2}}…
Question Number 154202 by mathdanisur last updated on 15/Sep/21 $$\boldsymbol{\Omega}\:\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{ln}\centerdot\left(\mathrm{1}\:+\:\mathrm{x}\right)}{\mathrm{x}\centerdot\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}\right)}\:\mathrm{dx}\:=\:? \\ $$ Answered by qaz last updated on 15/Sep/21 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{x}\left(\mathrm{x}^{\mathrm{2}}…
Question Number 88642 by M±th+et£s last updated on 11/Apr/20 Commented by ajfour last updated on 11/Apr/20 $${x}=\frac{\pi}{\mathrm{4}}\:,\:\:{of}\:{course}\:{qualifies}. \\ $$$${both}\:{terms}\:{are}\:{zero}. \\ $$ Commented by M±th+et£s last…
Question Number 154177 by EDWIN88 last updated on 15/Sep/21 Commented by Tawa11 last updated on 15/Sep/21 $$\mathrm{nice} \\ $$ Commented by EDWIN88 last updated on…
Question Number 23096 by tawa tawa last updated on 26/Oct/17 $$\mathrm{Solve}:\:\:\mathrm{3}^{\mathrm{x}\:} =\:\frac{\mathrm{27}}{\mathrm{x}}\:+\:\mathrm{18} \\ $$ Commented by Physics lover last updated on 26/Oct/17 $${i}\:{just}\:{used}\:{hit}\:{and}\:{trial}\:{method} \\ $$$${and}\:{got}\:{x}\:=\:\mathrm{3}…