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Category: Algebra

Question-18149

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}…

if-x-y-z-gt-0-and-xyz-1-prove-that-x-4-x-yz-y-4-y-zx-z-4-z-xy-3-2-

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-149219

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}} \\…

If-loga-and-logb-are-the-roots-of-the-equation-mx-2-nx-s-0-fimd-in-terms-of-m-n-and-s-the-value-of-logab-

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-149192

Question Number 149192 by Samimsultani last updated on 03/Aug/21 Answered by prakash jain last updated on 03/Aug/21 $$\left(\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}\right)^{{x}} ={u} \\ $$$$\left(\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}\right)^{{x}} =\frac{\mathrm{1}}{{u}} \\ $$$${u}−\frac{\mathrm{1}}{{u}}=\mathrm{40}\sqrt{\mathrm{6}} \\…