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Category: Algebra

Please-is-there-any-way-to-reduce-a-polynomial-of-4th-degree-and-solve-Or-probably-a-polynomial-of-nth-power-to-smaller-power-

Question Number 56479 by Tawa1 last updated on 17/Mar/19 $$\mathrm{Please}\:\mathrm{is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{way}\:\mathrm{to}\:\mathrm{reduce}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{of}\:\:\mathrm{4th}\:\mathrm{degree} \\ $$$$\mathrm{and}\:\mathrm{solve}.\:\:\mathrm{Or}\:\mathrm{probably}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{of}\:\:\:\mathrm{nth}\:\mathrm{power}\:\mathrm{to}\:\mathrm{smaller} \\ $$$$\mathrm{power}.\: \\ $$ Answered by ajfour last updated on 17/Mar/19 $$ \\…

Solve-the-system-of-equations-x-2-y-2-2xy-x-y-1-x-y-x-2-y-in-real-numbers-x-y-

Question Number 122002 by liberty last updated on 13/Nov/20 $$\:\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations}\: \\ $$$$\begin{cases}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\frac{\mathrm{2xy}}{\mathrm{x}+\mathrm{y}}\:=\:\mathrm{1}}\\{\sqrt{\mathrm{x}+\mathrm{y}}\:=\:\mathrm{x}^{\mathrm{2}} −\mathrm{y}}\end{cases}\:\mathrm{in}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{x},\mathrm{y}. \\ $$ Answered by MJS_new last updated on 13/Nov/20 $$\sqrt{{x}+{y}}={x}^{\mathrm{2}}…

x-2x-4x-8x-16x-32x-123456-find-all-values-of-x-for-which-this-relation-holds-

Question Number 121996 by Anuragkar last updated on 13/Nov/20 $$\lfloor{x}\rfloor\:+\lfloor\mathrm{2}{x}\rfloor+\lfloor\mathrm{4}{x}\rfloor+\lfloor\mathrm{8}{x}\rfloor+\lfloor\mathrm{16}{x}\rfloor+\lfloor\mathrm{32}{x}\rfloor=\mathrm{123456} \\ $$$${find}\:{all}\:{values}\:{of}\:{x}\:{for}\:{which}\:{this}\:{relation}\:{holds}? \\ $$ Answered by prakash jain last updated on 13/Nov/20 $${x}={n}+{f} \\ $$$${n}\left(\mathrm{1}+\mathrm{2}+\mathrm{4}+…+\mathrm{32}\right)…

solve-this-equation-xy-x-y-19-yz-y-z-11-z-x-zx-14-

Question Number 121973 by bemath last updated on 13/Nov/20 $$\:{solve}\:{this}\:{equation}\: \\ $$$$\:\begin{cases}{{xy}+{x}+{y}=\mathrm{19}}\\{{yz}\:+\:{y}+{z}\:=\:\mathrm{11}}\\{{z}+{x}+{zx}\:=\:\mathrm{14}}\end{cases} \\ $$ Commented by liberty last updated on 13/Nov/20 $$\rightarrow\:\mathrm{x}\left(\mathrm{y}+\mathrm{1}\right)=\mathrm{19}−\mathrm{y}\:\wedge\:\mathrm{z}\left(\mathrm{y}+\mathrm{1}\right)=\mathrm{11}−\mathrm{y} \\ $$$$\Rightarrow\begin{cases}{\mathrm{x}=\frac{\mathrm{19}−\mathrm{y}}{\mathrm{y}+\mathrm{1}}}\\{\mathrm{z}=\frac{\mathrm{11}−\mathrm{y}}{\mathrm{y}+\mathrm{1}}}\end{cases}\:\Leftrightarrow\:\mathrm{substitution}\:\mathrm{to}\:\mathrm{eq}\left(\mathrm{3}\right) \\…