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Question Number 143979 by mathdanisur last updated on 20/Jun/21 Answered by mitica last updated on 20/Jun/21 $${p}={x}+{y}+{z};{q}={xy}+{yz}+{xz};{r}={xyz}\Rightarrow{p}^{\mathrm{2}} \geqslant\mathrm{3}{q} \\ $$$$\mathrm{3}\left({p}+\frac{\mathrm{3}{r}}{{q}}\right)^{\mathrm{4}} =\mathrm{3}\left(\frac{{p}}{\mathrm{3}}+\frac{{p}}{\mathrm{3}}+\frac{{p}}{\mathrm{3}}+\frac{\mathrm{3}{r}}{{q}}\right)^{\mathrm{4}} \overset{{am}−{gm}} {\geqslant} \\ $$$$\geqslant\mathrm{3}\left(\mathrm{4}\centerdot\sqrt[{\mathrm{4}}]{\frac{{p}}{\mathrm{3}}\centerdot\frac{{p}}{\mathrm{3}}\centerdot\frac{{p}}{\mathrm{3}}\centerdot\frac{\mathrm{3}{r}}{{q}}}\right)^{\mathrm{4}}…
Question Number 78440 by ajfour last updated on 17/Jan/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ab}\:=\:{p} \\ $$$$\:\:\left({a}−\mathrm{2}{b}\right)\left({a}+{b}\right)\left({a}+\mathrm{2}{b}\right)=−\mathrm{24}{q} \\ $$$${Find}\:\:\:\frac{{a}+{b}}{\mathrm{3}}\:\:\:\:{in}\:{terms}\:{of}\:{p},\:{q}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 12889 by sin (x) last updated on 05/May/17 $${f}\left({x}−\mathrm{1}\right)=\frac{\mathrm{2}}{\mathrm{3}}+{f}\left({x}\right) \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{36}−{f}\left(\mathrm{21}\right) \\ $$$$\Rightarrow{f}\left(\mathrm{0}\right)=? \\ $$ Commented by prakash jain last updated on 06/May/17…
Question Number 12885 by FilupS last updated on 05/May/17 $${f}\left({f}\left({x}\right)\right)={f}^{\mathrm{2}} \left({x}\right) \\ $$$$\: \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}? \\ $$ Answered by mrW1 last updated on 05/May/17 $${u}={f}\left({x}\right)…
Question Number 12883 by FilupS last updated on 05/May/17 $$\mathrm{for}\:\:\:\:\:−\mathrm{128}\leqslant{x}\leqslant\mathrm{127} \\ $$$$\mathrm{and}\:\:\:−\mathrm{127}\leqslant{y}\leqslant\mathrm{128} \\ $$$$\mathrm{where}\:\:\:{x},{y}\in\mathbb{Z} \\ $$$$\: \\ $$$$\mathrm{Point}\:{P}\left({x},{y}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{cartesian}\:\mathrm{plane}. \\ $$$$\: \\ $$$$\mathrm{From}\:\mathrm{the}\:\mathrm{origin},\:\mathrm{angle}\:\theta\:\mathrm{is}\:\mathrm{made}\:\mathrm{counter} \\…
Question Number 78399 by john santu last updated on 17/Jan/20 $${dear}\:{sir}\:{W},\:{Mjs}\: \\ $$$${the}\:{set}\:\left\{\mathrm{1},\mathrm{4},{n}\right\}\:{have}\:{the}\:{condition}\:{that}\: \\ $$$${if}\:{two}\:{different}\:{elements}\:{are} \\ $$$${selected}\:{and}\:\mathrm{2112}\:{is}\:{added}\:{to} \\ $$$${the}\:{result}\:,\:{then}\:{the}\:{result}\: \\ $$$${is}\:{a}\:{perfect}\:{square}\:{if}\:{n}\:{is}\:{a}\: \\ $$$${positif}\:{number}\:.\:{then}\:{the}\:{number}\: \\ $$$${of}\:{possible}\:{values}\:{of}\:{n}\:{is}\:…
Question Number 78390 by mr W last updated on 17/Jan/20 $${solve}\:{for}\:\boldsymbol{{different}}\:{digits}\:{a},{b},{c},{d}\: \\ $$$${such}\:{that}\:\boldsymbol{{abcd}}=\left(\boldsymbol{{ab}}+\boldsymbol{{cd}}\right)^{\mathrm{2}} . \\ $$ Answered by MJS last updated on 17/Jan/20 $$\mathrm{0000} \\…
Question Number 143909 by mathdanisur last updated on 19/Jun/21 Commented by mr W last updated on 19/Jun/21 $${i}\:{remember}\:{i}\:{solved}\:{the}\:{same} \\ $$$${question}\:{some}\:{days}\:{ago}. \\ $$ Commented by amin96…
Question Number 143906 by mathdanisur last updated on 19/Jun/21 Answered by TheHoneyCat last updated on 19/Jun/21 $$\Leftrightarrow{x}^{{x}} −{y}^{{y}} ={e}.\mathrm{ln}\left(\frac{{y}}{{x}}\right)={e}\left(\mathrm{ln}\left({y}\right)−\mathrm{ln}\left({x}\right)\right) \\ $$$$\Leftrightarrow{x}^{{x}} +{e}\mathrm{ln}{x}={y}^{{y}} +{e}\mathrm{ln}{y} \\ $$$$…