Question Number 149240 by john_santu last updated on 04/Aug/21 $$\:\:\mathrm{solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{number}\: \\ $$$$\:\mathrm{x}^{\mathrm{4}} −\mathrm{3x}^{\mathrm{2}} +\mathrm{1}\:=\sqrt{\frac{\mathrm{4}}{\mathrm{4}−\mathrm{x}^{\mathrm{2}} }\:−\mathrm{1}} \\ $$$$\:\: \\ $$ Answered by MJS_new last updated on…
Question Number 149238 by ajfour last updated on 04/Aug/21 $${z}^{\mathrm{3}} −{z}={c} \\ $$$${z}^{\mathrm{4}} −{z}^{\mathrm{2}} ={cz} \\ $$$${let}\:\:{z}={x}+{q} \\ $$$${x}^{\mathrm{4}} +\mathrm{4}{qx}^{\mathrm{3}} +\mathrm{6}{q}^{\mathrm{2}} {x}^{\mathrm{2}} +\mathrm{4}{q}^{\mathrm{3}} {x}+{q}^{\mathrm{4}} \\…
Question Number 149234 by mathdanisur last updated on 03/Aug/21 $$\frac{{x}}{\mathrm{2}}\:+\:{log}_{\mathrm{2}} \left({x}\:+\:\mathrm{12}\right)\:=\:\mathrm{6} \\ $$$$\Rightarrow\:\boldsymbol{{x}}\:=\:? \\ $$ Answered by JDamian last updated on 03/Aug/21 $$\mathrm{4} \\ $$…
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Question Number 18149 by b.e.h.i.8.3.417@gmail.com last updated on 15/Jul/17 Commented by mrW1 last updated on 16/Jul/17 $$\mathrm{an}\:\mathrm{other}\:\mathrm{try}: \\ $$$$\mathrm{let}\:\mathrm{u}=\mathrm{xyz} \\ $$$$\Rightarrow\mathrm{x}^{\mathrm{2}} +\mathrm{xyz}=\mathrm{17x} \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{17x}+\mathrm{u}=\mathrm{0}…
Question Number 149212 by mathdanisur last updated on 03/Aug/21 $${if}\:\:\:{x};{y};{z}>\mathrm{0}\:\:\:{and}\:\:\:{xyz}=\mathrm{1}\:\:\:{prove}\:{that}: \\ $$$$\frac{{x}^{\mathrm{4}} }{{x}+{yz}}\:+\:\frac{{y}^{\mathrm{4}} }{{y}+{zx}}\:+\:\frac{{z}^{\mathrm{4}} }{{z}+{xy}}\:\geqslant\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$ Answered by dumitrel last updated on 03/Aug/21 Commented…
Question Number 149219 by mathdanisur last updated on 03/Aug/21 Answered by mindispower last updated on 03/Aug/21 $$\:\:^{\mathrm{4}} \sqrt{\varphi}={x} \\ $$$$\Leftrightarrow\frac{\mathrm{2}}{{x}}+{x}^{\mathrm{2}} <\mathrm{1}+\frac{{x}^{\mathrm{2}} +{x}^{\mathrm{4}} +{x}^{\mathrm{3}} }{\mathrm{2}} \\…
Question Number 149208 by pete last updated on 03/Aug/21 $$\mathrm{If}\:\mathrm{loga}\:\mathrm{and}\:\mathrm{logb}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{mx}^{\mathrm{2}} +\mathrm{nx}+\mathrm{s}=\mathrm{0},\:\mathrm{fimd}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{m},\:\mathrm{n}\:\mathrm{and} \\ $$$$\mathrm{s}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{logab}. \\ $$ Answered by gsk2684 last updated on 03/Aug/21 $$\mathrm{log}\:{a}\:+\mathrm{log}\:{b}\:=−\frac{{n}}{{m}}…
Question Number 83674 by Power last updated on 05/Mar/20 Commented by Power last updated on 05/Mar/20 $$\mathrm{sir}\:\:\mathrm{MJS} \\ $$ Answered by mahdi last updated on…
Question Number 83672 by jagoll last updated on 05/Mar/20 $${x}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:=\:\mathrm{51}\: \\ $$$${find}\:{x}\: \\ $$ Answered by john santu last updated on 05/Mar/20 $${x}^{\mathrm{2}}…