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Author: Tinku Tara

f-x-4-3-2-1-3-

Question Number 8794 by faster1998 last updated on 28/Oct/16 $${f}\left({x}\right)=×^{\frac{\mathrm{4}}{\mathrm{3}}} −\mathrm{2}×^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$ Commented by ridwan balatif last updated on 28/Oct/16 $$\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}} .\mathrm{x}−\mathrm{2x}^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}}…

Question-74328

Question Number 74328 by arthur.kangdani@gmail.com last updated on 22/Nov/19 Answered by ajfour last updated on 22/Nov/19 $${x}=\frac{\begin{vmatrix}{\mathrm{10}}&{\mathrm{2}}&{\mathrm{4}}\\{\mathrm{4}}&{\mathrm{10}}&{\mathrm{7}}\\{\mathrm{9}}&{\mathrm{5}}&{\mathrm{16}}\end{vmatrix}_{} }{\begin{vmatrix}{\mathrm{6}}&{\mathrm{2}}&{\mathrm{4}}\\{\mathrm{9}}&{\mathrm{10}}&{\mathrm{7}}\\{\mathrm{12}}&{\mathrm{5}}&{\mathrm{16}}\end{vmatrix}^{} } \\ $$$$\Rightarrow\:\:{x}=\frac{\mathrm{10}\left(\mathrm{160}−\mathrm{35}\right)−\mathrm{2}\left(\mathrm{64}−\mathrm{63}\right)+\mathrm{4}\left(\mathrm{20}−\mathrm{90}\right)}{\mathrm{6}\left(\mathrm{160}−\mathrm{35}\right)−\mathrm{2}\left(\mathrm{144}−\mathrm{84}\right)+\mathrm{4}\left(\mathrm{45}−\mathrm{120}\right)} \\ $$$$\:\:\:\:\:{x}=\frac{\mathrm{1250}−\mathrm{2}−\mathrm{280}}{\mathrm{750}−\mathrm{120}−\mathrm{300}}\:=\:\frac{\mathrm{968}}{\mathrm{330}}\:=\:\frac{\mathrm{88}}{\mathrm{30}} \\ $$$$…..…

2z-1-1-3-8z-4-1-5-16-

Question Number 139861 by mathdanisur last updated on 01/May/21 $$\sqrt[{\mathrm{3}}]{\mathrm{2}\boldsymbol{{z}}+\mathrm{1}}\:+\:\sqrt[{\mathrm{5}}]{\mathrm{8}\boldsymbol{{z}}+\mathrm{4}}\:=\:\sqrt{\mathrm{16}} \\ $$ Answered by mindispower last updated on 01/May/21 $${z}=\frac{\mathrm{7}}{\mathrm{2}},{solution} \\ $$$${over}\:\mathbb{R} \\ $$$${f}\left({z}\right)=\sqrt[{\mathrm{3}}]{\mathrm{2}{z}+\mathrm{1}}+\sqrt[{\mathrm{5}}]{\mathrm{8}{z}+\mathrm{4}}\:{is}\:{increase}\:{function} \\…

Find-the-general-solution-of-the-equation-dy-dx-2xy-y-2-x-2-2xy-

Question Number 8789 by tawakalitu last updated on 27/Oct/16 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{2xy}\:+\:\mathrm{y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2xy}} \\ $$ Commented by Yozzias last updated on 27/Oct/16 $$\mathrm{Let}\:\mathrm{y}=\mathrm{ux}\Rightarrow\mathrm{y}'=\mathrm{u}+\mathrm{xu}' \\…

Let-k-xy-yz-zx-x-y-z-x-y-y-z-z-x-Find-the-minimum-and-maximum-value-of-k-

Question Number 74322 by naka3546 last updated on 22/Nov/19 $${Let}\:\: \\ $$$${k}\:\:=\:\:\frac{\left({xy}\:+\:{yz}\:+\:{zx}\right)\left({x}\:+\:{y}\:+\:{z}\right)}{\left({x}\:+\:{y}\right)\left({y}\:+\:{z}\right)\left({z}\:+\:{x}\right)} \\ $$$${Find}\:\:{the}\:\:{minimum}\:\:{and}\:\:{maximum}\:\:{value}\:\:{of}\:\:\:{k}\:. \\ $$ Answered by MJS last updated on 23/Nov/19 $${k}−\mathrm{1}=\frac{{xyz}}{\left({x}+{y}\right)\left({x}+{z}\right)\left({y}+{z}\right)} \\…