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Author: Tinku Tara

Determine-a-b-c-Lazy-problem-J181-2-x-3-6x-2-15x-7-x-a-3-bx-c-J182-1-x-3-ax-2-x-1-x-2-bx-c-

Question Number 215730 by MathematicalUser2357 last updated on 16/Jan/25 $$\boldsymbol{\mathrm{Determine}}\:\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}}\:\left[\mathrm{Lazy}\:\mathrm{problem}\right] \\ $$$$\mathrm{J181}-\mathrm{2}.\:{x}^{\mathrm{3}} −\mathrm{6}{x}^{\mathrm{2}} +\mathrm{15}{x}−\mathrm{7}=\left({x}+{a}\right)^{\mathrm{3}} +{bx}+{c} \\ $$$$\mathrm{J182}-\left(\mathrm{1}\right)\:{x}^{\mathrm{3}} +{ax}+\mathrm{2}=\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +{bx}+{c}\right) \\ $$ Answered by A5T last…

Question-215708

Question Number 215708 by essaad last updated on 15/Jan/25 Answered by A5T last updated on 15/Jan/25 $$\left(\mathrm{i}\right)+\left(\mathrm{ii}\right)\Rightarrow\mathrm{n}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} =\mathrm{0}\Rightarrow\left(\mathrm{n}+\mathrm{y}\right)\left(\mathrm{n}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{ny}\right)=\mathrm{0}…\left(\mathrm{iii}\right) \\ $$$$\left(\mathrm{i}\right)−\left(\mathrm{ii}\right)\Rightarrow\mathrm{4n}^{\mathrm{3}} −\mathrm{4y}^{\mathrm{3}} −\mathrm{8n}+\mathrm{8y}=\mathrm{0}…

Question-215696

Question Number 215696 by BaliramKumar last updated on 15/Jan/25 Answered by MATHEMATICSAM last updated on 15/Jan/25 $$\mathrm{sec}^{\mathrm{4}} \mathrm{x}\:−\:\mathrm{cosec}^{\mathrm{4}} \mathrm{x}\:−\:\mathrm{2sec}^{\mathrm{2}} \mathrm{x}\:+\:\mathrm{2cosec}^{\mathrm{2}} \mathrm{x}\:=\:\frac{\mathrm{63}}{\mathrm{8}} \\ $$$$\Rightarrow\:\mathrm{sec}^{\mathrm{2}} {x}\left(\mathrm{sec}^{\mathrm{2}} {x}\:−\:\mathrm{2}\right)\:+\:\mathrm{cosec}^{\mathrm{2}}…

Question-215679

Question Number 215679 by BaliramKumar last updated on 14/Jan/25 Answered by MATHEMATICSAM last updated on 14/Jan/25 $$\mathrm{sec}^{\mathrm{2}} \theta\:=\:\frac{\mathrm{4}{xy}}{\left({x}\:+\:{y}\right)^{\mathrm{2}} } \\ $$$$\Rightarrow\:\mathrm{cos}^{\mathrm{2}} \theta\:=\:\frac{\left({x}\:+\:{y}\right)^{\mathrm{2}} }{\mathrm{4}{xy}} \\ $$$$\left({x}\:−\:{y}\right)^{\mathrm{2}}…

lim-x-1-sec-pi-2-x-arctanx-pi-4-

Question Number 215667 by mathlove last updated on 14/Jan/25 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{sec}\left(\frac{\pi}{\mathrm{2}}{x}\right)\left({arctanx}−\frac{\pi}{\mathrm{4}}\right)=? \\ $$ Answered by issac last updated on 14/Jan/25 $$\mathrm{sec}\left(\frac{\pi}{\mathrm{2}}\right)\left(\mathrm{arctan}\left(\mathrm{1}\right)−\frac{\pi}{\mathrm{4}}\right) \\ $$ Commented by…