Question Number 89451 by jagoll last updated on 17/Apr/20 $$\mathrm{log}_{\mathrm{5}} \:\left(\left(\mathrm{3}−{x}\right)\left({x}^{\mathrm{2}} +\mathrm{2}\right)\right)\:\geqslant\:\mathrm{log}_{\mathrm{5}} \left({x}^{\mathrm{2}} −\mathrm{7}{x}+\mathrm{12}\right)+\mathrm{log}_{\mathrm{5}} \left(\mathrm{5}−{x}\right) \\ $$ Answered by john santu last updated on 17/Apr/20…
Question Number 154987 by tabata last updated on 24/Sep/21 $$\int_{\mathrm{0}} ^{\:\infty} \:\frac{{x}^{{c}} }{{c}^{{x}} }\:\:{dx} \\ $$ Commented by talminator2856791 last updated on 24/Sep/21 $$\:\mathrm{the}\:\mathrm{integral}\:\mathrm{diverges}\:\mathrm{for}\:{c}\:\in\:\left(\mathrm{0},\mathrm{1}\right)\: \\…
Question Number 154986 by mathdanisur last updated on 23/Sep/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}\:\mathrm{in}\:\mathbb{R} \\ $$$$\mathrm{2x}\:=\:\frac{\mathrm{y}^{\mathrm{2}} \:-\:\mathrm{4y}\:+\:\mathrm{1}}{\mathrm{y}^{\mathrm{2}} \:-\:\mathrm{y}\:+\:\mathrm{1}} \\ $$$$\mathrm{y}\:=\:\frac{-\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{6x}\:-\:\mathrm{1}}{\mathrm{3x}^{\mathrm{2}} \:-\:\mathrm{2x}\:+\:\mathrm{3}} \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 89446 by I want to learn more last updated on 17/Apr/20 $$.. \\ $$ Commented by I want to learn more last updated…
Question Number 154980 by mathdanisur last updated on 23/Sep/21 $$\mathrm{if}\:\:\boldsymbol{\mathrm{a}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{b}}\:\:\mathrm{are}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\mathrm{determine}\:\mathrm{a}\:\mathrm{necessary}\:\mathrm{and}\:\mathrm{sufficient} \\ $$$$\mathrm{condition}\:\mathrm{so}\:\mathrm{as}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\frac{\mathrm{a}\sqrt{\mathrm{b}}}{\mathrm{x}}\:=\:\mathrm{a}\:+\:\mathrm{b} \\ $$$$\mathrm{to}\:\mathrm{have}\:\mathrm{three}\:\mathrm{real}\:\mathrm{distinct}\:\mathrm{roots}. \\ $$ Answered by mr W…
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Question Number 154973 by mathdanisur last updated on 23/Sep/21 $$\mathrm{If}\:\:\mathrm{x}\:+\:\frac{\mathrm{7}}{\:\sqrt{\mathrm{x}}}\:=\:\mathrm{50} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expression} \\ $$$$\sqrt{\mathrm{x}}\:-\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}}}\:=\:? \\ $$ Answered by mr W last updated on 23/Sep/21 $${let}\:{t}=\sqrt{{x}}>\mathrm{0}…
Question Number 154972 by Rankut last updated on 23/Sep/21 $${if}\:{in}\:{a}\:{triangle}\:{ABC},\:{A}\:{and}\:{B} \\ $$$${are}\:{complementry},\:{then}\:{tanC}\:{is}….? \\ $$ Commented by mr W last updated on 23/Sep/21 $${A}+{B}=\mathrm{90}° \\ $$$${C}=\mathrm{180}°−\left({A}+{B}\right)=\mathrm{90}°…
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