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Category: Algebra

Find-the-number-of-triplets-x-a-b-where-x-is-a-real-number-and-a-b-belongs-to-the-set-1-2-3-4-5-6-7-8-9-such-that-x-2-a-x-b-0-where-x-denotes-the-fractional-part-of-real-number-x-

Question Number 122095 by Anuragkar last updated on 14/Nov/20 $${Find}\:{the}\:\:{number}\:{of}\:{triplets}\left({x}/{a}/{b}\right)\:{where}\:{x} \\ $$$${is}\:{a}\:{real}\:{number}\:{and}\:\left({a}/{b}\right)\:{belongs}\:{to}\:{the}\:{set} \\ $$$$\left\{\mathrm{1}/\mathrm{2}/\mathrm{3}/\mathrm{4}/\mathrm{5}/\mathrm{6}/\mathrm{7}/\mathrm{8}/\mathrm{9}\right\}\:{such}\:{that}\: \\ $$$$ \\ $$$${x}^{\mathrm{2}} −{a}\left\{{x}\right\}+{b}\:=\mathrm{0} \\ $$$${where}\:\left\{{x}\right\}\:{denotes}\:{the}\:{fractional}\:{part}\:{of}\:{real}\:{number}\:{x} \\ $$$$ \\ $$$$…

solve-x-1-y-1-1-x-1-y-5-

Question Number 122081 by bobhans last updated on 14/Nov/20 $$\:{solve}\:\begin{cases}{\mid{x}−\mathrm{1}\mid+\mid{y}−\mathrm{1}\mid=\mathrm{1}}\\{\mid{x}−\mathrm{1}\mid−{y}=−\mathrm{5}}\end{cases} \\ $$ Answered by mathmax by abdo last updated on 14/Nov/20 $$\Rightarrow\begin{cases}{\mid\mathrm{x}−\mathrm{1}\mid=\mathrm{y}−\mathrm{5}}\\{\mid\mathrm{y}−\mathrm{1}\mid+\mathrm{y}\:=\mathrm{6}\:\:\:\:\:\mathrm{let}\:\mathrm{solve}\:\mid\mathrm{y}−\mathrm{1}\mid+\mathrm{y}\:=\mathrm{6}\:\:\mathrm{withy}\geqslant\mathrm{5}}\end{cases} \\ $$$$\Rightarrow\mid\mathrm{y}−\mathrm{1}\mid+\mathrm{y}−\mathrm{6}=\mathrm{0} \\…

Question-122075

Question Number 122075 by peter frank last updated on 13/Nov/20 Answered by MJS_new last updated on 14/Nov/20 $$\mathrm{seriously}??? \\ $$$$=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\mid{x}+\mathrm{1}\mid{dx}=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left({x}+\mathrm{1}\right){dx}=\left[\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+{x}\right]_{\mathrm{0}}…

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}}…