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Category: Algebra

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Question Number 164650 by cortano1 last updated on 20/Jan/22 $$\:\:\sqrt[{\mathrm{3}}]{{x}+\mathrm{9}}\:−\sqrt[{\mathrm{3}}]{{x}−\mathrm{9}}\:=\:\mathrm{3}\: \\ $$$$\:{x}=? \\ $$ Answered by mr W last updated on 20/Jan/22 $$\left(\sqrt[{\mathrm{3}}]{\mathrm{9}+{x}}+\sqrt[{\mathrm{3}}]{\mathrm{9}−{x}}\right)^{\mathrm{3}} =\mathrm{3}^{\mathrm{3}} \\…

Given-f-x-x-3-ax-2-bx-c-with-a-b-c-R-the-roots-are-x-1-x-2-x-3-R-Let-is-an-positive-integer-that-satisfied-x-2-x-1-x-3-gt-1-2-x-1-x-2-What-is-the-max-value-o

Question Number 33569 by Joel578 last updated on 19/Apr/18 $$\mathrm{Given}\:{f}\left({x}\right)\:=\:{x}^{\mathrm{3}} \:+\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c} \\ $$$$\mathrm{with}\:{a},\:{b},\:{c}\:\in\:\mathbb{R},\:\mathrm{the}\:\mathrm{roots}\:\mathrm{are}\:{x}_{\mathrm{1}} ,\:{x}_{\mathrm{2}} ,\:{x}_{\mathrm{3}} \:\in\:\mathbb{R} \\ $$$$\mathrm{Let}\:\lambda\:\mathrm{is}\:\mathrm{an}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{that}\:\mathrm{satisfied} \\ $$$${x}_{\mathrm{2}} \:−\:{x}_{\mathrm{1}} \:=\:\lambda \\ $$$${x}_{\mathrm{3}}…

find-9-9-9-9-9-9-9-1-3-1-3-1-3-1-3-8-8-8-8-8-8-8-

Question Number 99094 by bemath last updated on 18/Jun/20 $$\mathrm{find}\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\mathrm{9}\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\mathrm{9}\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\mathrm{9}\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+…}}}}− \\ $$$$\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}+\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{}}}}…}}}}\: \\ $$ Answered by bobhans last updated on 18/Jun/20 $$\mathrm{y}\:=\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\mathrm{9y}}\:\Rightarrow\mathrm{y}^{\mathrm{3}} −\mathrm{9y}−\mathrm{9}\:=\:\mathrm{0} \\ $$$$\mathrm{x}=\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}+\mathrm{x}}}}\:\Rightarrow\:\mathrm{x}^{\mathrm{3}}…

9-9-9-9-1-3-1-3-1-3-1-3-8-8-8-8-

Question Number 99089 by bramlex last updated on 18/Jun/20 $$\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+…}}}}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−…}}}} \\ $$ Answered by MJS last updated on 18/Jun/20 $${a}=\sqrt[{\mathrm{3}}]{\mathrm{9}+\sqrt[{\mathrm{3}}]{\mathrm{9}+…}} \\ $$$${a}^{\mathrm{3}} =\mathrm{9}+{a} \\ $$$${a}^{\mathrm{3}}…