Question Number 150191 by mathdanisur last updated on 10/Aug/21 $$\begin{cases}{\mathrm{x}\:-\:\sqrt{\mathrm{y}}\:=\:\mathrm{7}}\\{\mathrm{y}\:+\:\sqrt{\mathrm{x}}\:=\:\mathrm{7}}\end{cases}\:\:\:\Rightarrow\:\:\mathrm{xy}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 10/Aug/21 $$\begin{cases}{\mathrm{x}\:-\:\underset{\mathrm{v}} {\underbrace{\sqrt{\mathrm{y}}}}\:=\:\mathrm{7}}\\{\mathrm{y}\:+\:\underset{\mathrm{u}} {\underbrace{\sqrt{\mathrm{x}}}}\:=\:\mathrm{7}}\end{cases}\:\:\:\Rightarrow\:\:\mathrm{xy}\:=\:? \\ $$$$\mathrm{u}^{\mathrm{2}} −\mathrm{v}=\mathrm{7}\:\wedge\:\mathrm{v}^{\mathrm{2}}…
Question Number 150187 by mathdanisur last updated on 10/Aug/21 $$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{2x}^{\mathrm{2}} \:+\:\mathrm{5}\:\:\Rightarrow\:\:\mathrm{f}^{\:−\mathrm{1}} \left(\mathrm{2}\right)\:=\:? \\ $$ Commented by amin96 last updated on 10/Aug/21 $$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}=\mathrm{2}\:\:\Rightarrow\:\:\:{x}=\pm\frac{\mathrm{3}{i}}{\:\sqrt{\mathrm{2}}}\:\:\: \\ $$$${f}\left(\pm\frac{\mathrm{3}{i}}{\:\sqrt{\mathrm{2}}}\right)=\mathrm{2}\:\:\:\:\Rightarrow\:\:{f}^{−\mathrm{1}}…
Question Number 150181 by liberty last updated on 10/Aug/21 $$\:\left(\mathrm{x}−\mathrm{6}\right)^{\mathrm{3}} +\left(\mathrm{x}−\mathrm{5}\right)^{\mathrm{3}} +\left(\mathrm{x}−\mathrm{4}\right)^{\mathrm{3}} =\mathrm{3}\left(\mathrm{x}−\mathrm{6}\right)\left(\mathrm{x}−\mathrm{5}\right)\left(\mathrm{x}−\mathrm{4}\right) \\ $$$$\mathrm{x}=? \\ $$ Answered by Rasheed.Sindhi last updated on 13/Aug/21 $$\:\left(\mathrm{x}−\mathrm{6}\right)^{\mathrm{3}}…
Question Number 150186 by mathdanisur last updated on 10/Aug/21 $$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{sin}^{\mathrm{4}} \left(\mathrm{3x}\right)\:\:\Rightarrow\:\:{f}\:^{'} \left(\frac{\pi}{\mathrm{12}}\right)\:=\:? \\ $$ Answered by puissant last updated on 10/Aug/21 $$\mathrm{f}'\left(\mathrm{x}\right)=\mathrm{4}×\mathrm{3cos}\left(\mathrm{3x}\right)\mathrm{sin}^{\mathrm{3}} \left(\mathrm{3x}\right) \\ $$$$\Rightarrow\:\mathrm{f}'\left(\mathrm{x}\right)=\mathrm{12cos}\left(\mathrm{3x}\right)\mathrm{sin}^{\mathrm{3}}…
Question Number 19101 by Tinkutara last updated on 04/Aug/17 $$\mathrm{A}\:\mathrm{polynomial}\:{f}\left({x}\right)\:\mathrm{with}\:\mathrm{rational} \\ $$$$\mathrm{coefficients}\:\mathrm{leaves}\:\mathrm{remainder}\:\mathrm{15},\:\mathrm{when} \\ $$$$\mathrm{divided}\:\mathrm{by}\:{x}\:−\:\mathrm{3}\:\mathrm{and}\:\mathrm{remainder}\:\mathrm{2}{x}\:+\:\mathrm{1}, \\ $$$$\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\left({x}\:−\:\mathrm{1}\right)^{\mathrm{2}} .\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{remainder}\:\mathrm{when}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by} \\ $$$$\left({x}\:−\:\mathrm{3}\right)\left({x}\:−\:\mathrm{1}\right)^{\mathrm{2}} . \\ $$ Commented…
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Question Number 19095 by khamizan833@yahoo.com last updated on 04/Aug/17 Commented by ajfour last updated on 04/Aug/17 $$\mathrm{abc}=\mathrm{18c}−\mathrm{c}^{\mathrm{3}} \:. \\ $$ Commented by khamizan833@yahoo.com last updated…
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Question Number 19063 by chux last updated on 03/Aug/17 $$\mathrm{find}\:\mathrm{the}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{if} \\ $$$$\frac{\mathrm{8}^{\mathrm{x}} +\mathrm{27}^{\mathrm{x}} }{\mathrm{12}^{\mathrm{x}} +\mathrm{18}^{\mathrm{x}} }=\frac{\mathrm{7}}{\mathrm{6}} \\ $$ Answered by 433 last updated on 03/Aug/17…
Question Number 84588 by john santu last updated on 14/Mar/20 $$\mathrm{if}\:\mathrm{x}\:−\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\mathrm{9} \\ $$$$\mathrm{x}^{\mathrm{3}} −\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\:=\:? \\ $$ Answered by john santu last updated on 14/Mar/20…