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Category: Algebra

show-that-x-is-small-enough-for-its-cube-and-higher-power-to-be-neghected-1-x-1-x-1-x-1-2-x-2-by-putting-1-8-show-that-7-2-83-128-

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…

the-expression-ax-2-bx-c-is-divisible-by-x-1-has-reminder-2-when-divided-by-x-1-and-has-reminder-8-when-divided-by-x-2-find-the-value-of-a-b-and-c-

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-75110

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}}…

2-3-x-7-4-3-2-3-x-4-2-3-x-0-What-is-the-value-of-x-

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}} \\…

1-x-xdx-

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}…

1-x-2023-1-x-x-2-2022-a-0-a-1-x-a-2-x-2-a-6067-x-6067-also-if-the-equations-a-n-1-mod-5-a-n-2-mod-5-n-0-1-2-6067-has-u-and-v-solutions-respectivley-then-prove-that-

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} \\…