Question Number 9576 by j.masanja06@gmail.com last updated on 18/Dec/16 $$\mathrm{show}\:\mathrm{that}\:\mathrm{x}\:\mathrm{is}\:\mathrm{small}\:\mathrm{enough}\:\mathrm{for}\:\mathrm{its}\:\mathrm{cube}\:\mathrm{and}\:\mathrm{higher}\:\mathrm{power}\:\mathrm{to}\:\mathrm{be}\:\mathrm{neghected} \\ $$$$\sqrt{\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}}=\mathrm{1}−\mathrm{x}+\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}^{\mathrm{2}} . \\ $$$$\mathrm{by}\:\mathrm{putting}\:=\frac{\mathrm{1}}{\mathrm{8}},\mathrm{show}\:\mathrm{that}\:\sqrt{\mathrm{7}}\approx\mathrm{2}\frac{\mathrm{83}}{\mathrm{128}}. \\ $$ Commented by prakash jain last updated on 20/Dec/16…
Question Number 9575 by j.masanja06@gmail.com last updated on 18/Dec/16 $$\mathrm{the}\:\mathrm{expression}\:\mathrm{ax}^{\mathrm{2}} \:+\:\mathrm{bx}\:+\:\mathrm{c}\:\mathrm{is}\:\mathrm{divisible}\:\:\mathrm{by}\:\mathrm{x}−\mathrm{1},\mathrm{has}\:\mathrm{reminder}\:\mathrm{2}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{x}+\mathrm{1},\mathrm{and}\:\mathrm{has}\:\mathrm{reminder}\:\mathrm{8}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{x}−\mathrm{2}.\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a},\mathrm{b}\:\mathrm{and}\:\mathrm{c}. \\ $$ Commented by ridwan balatif last updated on 18/Dec/16 $$\mathrm{P}\left(\mathrm{x}\right)\equiv\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c} \\ $$$$\left(\mathrm{x}−\mathrm{1}\right)\mathrm{is}\:\mathrm{divisible}\:\mathrm{P}\left(\mathrm{x}\right)\rightarrow\mathrm{P}\left(\mathrm{1}\right)=\mathrm{0}…
Question Number 75110 by peter frank last updated on 07/Dec/19 Answered by mind is power last updated on 08/Dec/19 $$\mathrm{ax}+\mathrm{by}+\mathrm{c}=\mathrm{0} \\ $$$$\mathrm{x}=\mathrm{0}\Rightarrow\mathrm{y}_{\mathrm{0}} =−\frac{\mathrm{c}}{\mathrm{b}}…..\mathrm{b}\neq\mathrm{0} \\ $$$$\mathrm{y}=\mathrm{0}\Rightarrow\mathrm{x}_{\mathrm{0}}…
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Question Number 9548 by Joel575 last updated on 14/Dec/16 $${a}\:−\:\mathrm{7}{b}\:+\:\mathrm{8}{c}\:=\:\mathrm{4} \\ $$$$\mathrm{8}{a}\:+\:\mathrm{4}{b}\:−\:{c}\:=\:\mathrm{7} \\ $$$${a},\:{b},\:{c}\:\in\:\mathbb{R} \\ $$$$ \\ $$$$\mathrm{60}\left({a}^{\mathrm{2}} \:−\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \right)\:=\:? \\ $$ Answered by…
Question Number 9543 by Joel575 last updated on 14/Dec/16 $$\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{{x}} \:+\:\left(\mathrm{7}−\mathrm{4}\sqrt{\mathrm{3}}\right)\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{{x}} \:=\:\mathrm{4}\left(\mathrm{2}−\sqrt{\mathrm{3}}\right),\:{x}\:\neq\:\mathrm{0} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:?\: \\ $$ Answered by mrW last updated on 14/Dec/16 $$\mathrm{u}=\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{x}} \\…
Question Number 9541 by FilupSmith last updated on 14/Dec/16 $$\int\left(−\mathrm{1}\right)^{{x}} {xdx}=?? \\ $$ Answered by FilupSmith last updated on 15/Dec/16 $$\int\left(−\mathrm{1}\right)^{{x}} {xdx}=\int{e}^{{x}\mathrm{ln}\left(−\mathrm{1}\right)} {xdx} \\ $$$$=\int{e}^{{xi}\pi}…
Question Number 140606 by mathsuji last updated on 10/May/21 $$\left(\mathrm{1}+{x}\right)^{\mathrm{2023}} \left(\mathrm{1}−{x}+{x}^{\mathrm{2}} \right)^{\mathrm{2022}} ={a}_{\mathrm{0}} +{a}_{\mathrm{1}} {x}+{a}_{\mathrm{2}} {x}^{\mathrm{2}} +…+{a}_{\mathrm{6067}} {x}^{\mathrm{6067}} \\ $$$${also}\:{if}\:{the}\:{equations} \\ $$$${a}_{{n}} \equiv\:\mathrm{1}\left({mod}\:\mathrm{5}\right)\:,\:{a}_{{n}} \equiv\:\mathrm{2}\left({mod}\:\mathrm{5}\right)\:,\:{n}=\mathrm{0};\mathrm{1};\mathrm{2};…;\mathrm{6067} \\…
Question Number 9533 by FilupSmith last updated on 14/Dec/16 $$\mathrm{Determine}\:\mathrm{and}\:\mathrm{prove}\:\mathrm{if}\:\mathrm{true}: \\ $$$$\int_{\mathrm{0}} ^{\:{n}} {x}^{\mathrm{2}} {dx}\:<\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{\mathrm{2}} \\ $$ Answered by geovane10math last updated on…