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Category: Algebra

a-b-c-are-the-roots-from-equation-x-3-5x-2-9x-10-0-If-P-x-Ax-3-Bx-2-Cx-2015-and-P-a-b-c-P-b-a-c-P-c-a-b-What-is-the-value-of-A-B-C-

Question Number 11753 by Joel576 last updated on 31/Mar/17 $${a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{from}\:\mathrm{equation}\:{x}^{\mathrm{3}} \:−\:\mathrm{5}{x}^{\mathrm{2}} \:−\:\mathrm{9}{x}\:+\:\mathrm{10}\:=\:\mathrm{0} \\ $$$$\mathrm{If}\:{P}\left({x}\right)\:=\:{Ax}^{\mathrm{3}} \:+\:{Bx}^{\mathrm{2}} \:+\:{Cx}\:−\:\mathrm{2015}\:\mathrm{and} \\ $$$${P}\left({a}\right)\:=\:{b}\:+\:{c}\: \\ $$$${P}\left({b}\right)\:=\:{a}\:+\:{c} \\ $$$${P}\left({c}\right)\:=\:{a}\:+\:{b} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{A}\:+\:{B}\:+\:{C}\:? \\…

Question-142822

Question Number 142822 by aupo14 last updated on 05/Jun/21 Answered by MJS_new last updated on 06/Jun/21 $${x}^{\mathrm{2}} ={i}+{x}\:\Rightarrow\:{x}=\frac{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{4i}}}{\mathrm{2}}=\frac{\mathrm{2}+\sqrt{\mathrm{2}\left(\mathrm{1}+\sqrt{\mathrm{17}}\right)}}{\mathrm{4}}+\frac{\sqrt{\mathrm{2}\left(−\mathrm{1}+\sqrt{\mathrm{17}}\right)}}{\mathrm{4}}\mathrm{i} \\ $$$$\mathrm{the}\:\mathrm{other}\:\mathrm{solution}\:\mathrm{doesn}'\mathrm{t}\:\mathrm{fit}\:\left(\mathrm{just}\:\mathrm{give}\:\mathrm{it}\:\mathrm{a}\:\mathrm{try}\right) \\ $$ Terms of Service…

Solve-simultaneously-x-2-4y-2-xy-6-equation-i-3x-2-8y-2-14-equation-ii-

Question Number 11748 by tawa last updated on 30/Mar/17 $$\mathrm{Solve}\:\mathrm{simultaneously} \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4y}^{\mathrm{2}} \:+\:\mathrm{xy}\:=\:\mathrm{6}\:\:\:\:\:…………..\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{8y}^{\mathrm{2}} \:=\:\mathrm{14}\:\:\:\:\:\:\:\:\:\:\:…………..\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$ Answered by mrW1 last updated…

xtan-2-x-dx-

Question Number 11741 by uni last updated on 30/Mar/17 $$\int\mathrm{xtan}^{\mathrm{2}} \:\mathrm{x}\:\mathrm{dx}=? \\ $$ Answered by mrW1 last updated on 30/Mar/17 $$\int{x}\mathrm{tan}^{\mathrm{2}} \:{x}\:{dx}=\int\mathrm{tan}^{\mathrm{2}} \:{x}\:{d}\left(\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\right) \\…

is-there-a-general-solution-for-the-equation-x-x-x-x-n-times-x-m-with-x-gt-0-m-gt-0-

Question Number 77204 by mr W last updated on 04/Jan/20 $${is}\:{there}\:{a}\:{general}\:{solution}\:{for} \\ $$$${the}\:{equation} \\ $$$$\underset{{n}\:{times}\:{x}} {\boldsymbol{{x}}\left[\boldsymbol{{x}}\left[\boldsymbol{{x}}\left[\boldsymbol{{x}}…\right]\right]\right]}=\boldsymbol{{m}} \\ $$$${with}\:{x}>\mathrm{0},\:{m}>\mathrm{0}. \\ $$ Commented by MJS last updated…

a-b-c-b-a-c-c-a-b-a-b-c-12-b-c-a-c-a-b-

Question Number 142740 by mathdanisur last updated on 04/Jun/21 $$\frac{{a}}{{b}+{c}}\:=\:\frac{{b}}{{a}+{c}}\:=\:\frac{{c}}{{a}+{b}}\:\:;\:\:{a}\centerdot{b}\centerdot{c}\:=\:\mathrm{12} \\ $$$$\left({b}+{c}\right)\centerdot\left({a}+{c}\right)\centerdot\left({a}+{b}\right)\:=\:? \\ $$ Commented by MJS_new last updated on 05/Jun/21 $$\mathrm{I}\:\mathrm{found}\:\mathrm{2}\:\mathrm{possibilities} \\ $$$$\left(\mathrm{1}\right)\:{a}={b}={c}=\sqrt[{\mathrm{3}}]{\mathrm{12}}\:\Rightarrow\:\mathrm{answer}\:\mathrm{is}\:\mathrm{96} \\…