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Category: Algebra

Solve-the-equation-x-x-x-x-x-x-x-x-where-x-gt-0-

Question Number 161563 by HongKing last updated on 19/Dec/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\:…}}}\:=\:\mathrm{x}\centerdot\sqrt{\mathrm{x}\centerdot\sqrt{\mathrm{x}\centerdot\sqrt{\mathrm{x}\centerdot\:…}}} \\ $$$$\mathrm{where}\:,\:\mathrm{x}>\mathrm{0} \\ $$ Answered by MJS_new last updated on 20/Dec/21 $$\mathrm{lhs}=\left(\mathrm{lhs}−{x}\right)^{\mathrm{2}} \wedge\mathrm{lhs}\geqslant{x}\:\Rightarrow\:\mathrm{lhs}=\frac{\mathrm{2}{x}+\mathrm{1}+\sqrt{\mathrm{4}{x}+\mathrm{1}}}{\mathrm{2}}…

if-p-and-q-are-two-complex-number-and-p-q-m-m-is-a-real-number-is-there-always-exists-a-p-1-3-and-q-1-3-we-know-p-1-3-and-q-1-3-each-has-actually-3-values-such-that-p-1-3-q-1-3

Question Number 96021 by SmNayon11 last updated on 29/May/20 $$\mathrm{if}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{are}\:\mathrm{two}\:\mathrm{complex}\:\mathrm{number} \\ $$$$\mathrm{and}\:\mathrm{p}×\mathrm{q}=\mathrm{m}\:\:,\mathrm{m}\:\mathrm{is}\:\mathrm{a}\:\mathrm{real}\:\mathrm{number}\:. \\ $$$$ \\ $$$$\mathrm{is}\:\mathrm{there}\:\mathrm{always}\:\mathrm{exists}\:\mathrm{a}\:\:\mathrm{p}^{\frac{\mathrm{1}}{\mathrm{3}}} \:\mathrm{and}\:\mathrm{q}^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$$\left(\mathrm{we}\:\mathrm{know}\:\mathrm{p}^{\frac{\mathrm{1}}{\mathrm{3}}} \:\mathrm{and}\:\mathrm{q}^{\frac{\mathrm{1}}{\mathrm{3}}} \mathrm{each}\:\mathrm{has}\:\mathrm{actually}\:\right. \\ $$$$\left.\mathrm{3}\:\mathrm{values}\right) \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{p}^{\frac{\mathrm{1}}{\mathrm{3}}}…

proof-that-a-2-a-b-a-c-b-2-b-c-b-a-c-2-c-a-c-b-a-b-c-

Question Number 30456 by daffa123 last updated on 22/Feb/18 $${proof}\:{that} \\ $$$$\frac{{a}^{\mathrm{2}} }{\left({a}−{b}\right)\left({a}−{c}\right)}+\frac{{b}^{\mathrm{2}} }{\left({b}−{c}\right)\left({b}−{a}\right)}+\frac{{c}^{\mathrm{2}} }{\left({c}−{a}\right)\left({c}−{b}\right)}=\:{a}+{b}+{c} \\ $$ Answered by Rasheed.Sindhi last updated on 22/Feb/18 $$\frac{{a}^{\mathrm{2}}…

x-6-6x-5-ax-4-bx-3-cx-2-dx-1-0-all-the-roots-of-the-equation-are-positive-find-a-b-c-d-

Question Number 161500 by HongKing last updated on 18/Dec/21 $$\mathrm{x}^{\mathrm{6}} \:-\:\mathrm{6x}^{\mathrm{5}} \:+\:\mathrm{ax}^{\mathrm{4}} \:+\:\mathrm{bx}^{\mathrm{3}} \:+\:\mathrm{cx}^{\mathrm{2}} \:+\:\mathrm{dx}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{all}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{are}\:\mathrm{positive} \\ $$$$\mathrm{find}\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}=? \\ $$ Answered by mr W…