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Category: Algebra

Question-35152

Question Number 35152 by Victor31926 last updated on 16/May/18 Commented by Rasheed.Sindhi last updated on 16/May/18 $$\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{1}……………\mathrm{I} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{35}……….\mathrm{II} \\ $$$$\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}}…

Question-35153

Question Number 35153 by Victor31926 last updated on 16/May/18 Answered by Rasheed.Sindhi last updated on 16/May/18 $$\mathrm{2}=\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+….}}} \\ $$$$\mathrm{2}−\mathrm{x}=\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+….}}} \\ $$$$\left(\mathrm{2}−\mathrm{x}\right)^{\mathrm{2}} =\left(\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+….}}}\right)^{\mathrm{2}} \\ $$$$\mathrm{4}−\mathrm{4x}+\mathrm{x}^{\mathrm{2}} =\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+….}}}…

Question-166215

Question Number 166215 by mathlove last updated on 15/Feb/22 Answered by nurtani last updated on 15/Feb/22 $$\bullet\:\mathrm{27}^{{x}} −\mathrm{27}^{{y}} \:=\:\mathrm{24}\:\Leftrightarrow\:\mathrm{3}^{\mathrm{3}{x}} −\mathrm{3}^{\mathrm{3}{y}} \:=\:\mathrm{24}\:\Leftrightarrow\:\left(\mathrm{3}^{{x}} \right)^{\mathrm{3}} −\left(\mathrm{3}^{{y}} \right)^{\mathrm{3}} =\:\mathrm{24}…

x-2-x-lt-2-x-find-solution-set-

Question Number 100660 by bobhans last updated on 28/Jun/20 $$\mid{x}^{\mathrm{2}} −{x}\mid\:<\:\mathrm{2}+{x}\:.\:{find}\:{solution}\:{set}. \\ $$ Commented by bramlex last updated on 28/Jun/20 $${since}\:\mid{x}^{\mathrm{2}} −{x}\mid\:\geqslant\mathrm{0}\:{then}\:\mathrm{2}+{x}\:{must}\:{be}\:>\mathrm{0} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{2}+{x}\:>\:\mathrm{0}\:;\:{x}\:>−\mathrm{2} \\…

n-1-m-1-1-m-2-n-mn-2-2mn-

Question Number 166160 by cortano1 last updated on 14/Feb/22 $$\:\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{\mathrm{m}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{m}^{\mathrm{2}} \mathrm{n}+\mathrm{mn}^{\mathrm{2}} +\mathrm{2mn}}=? \\ $$ Answered by Jamshidbek last updated on 14/Feb/22…

Question-100622

Question Number 100622 by MJS last updated on 27/Jun/20 Commented by MJS last updated on 27/Jun/20 $$\mathrm{building}\:\mathrm{on}\:\mathrm{my}\:\mathrm{work},\:\mathrm{can}\:\mathrm{someone}\:\mathrm{try}\:\mathrm{to} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{for}\:{x}\in\mathbb{Q}\:\mathrm{and} \\ $$$${x}\left[{x}\left[{x}\left[{x}\right]\right]\right]={n}\in\mathbb{N}\:? \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{picture},\:{i}\:\mathrm{and}\:{f}\:\mathrm{are}\:\mathrm{the}\:\mathrm{integer}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{fractional}\:\mathrm{part}\:\mathrm{of}\:{x}…

If-a-b-c-b-c-a-c-a-b-1-then-prove-that-a-2-b-c-b-2-c-a-c-2-a-b-0-

Question Number 35080 by math1967 last updated on 15/May/18 $${If}\:\frac{{a}}{{b}+{c}}\:+\frac{{b}}{{c}+{a}}\:+\frac{{c}}{{a}+{b}}=\mathrm{1}\:{then}\:{prove}\:{that} \\ $$$$\frac{{a}^{\mathrm{2}} }{{b}+{c}}\:+\frac{{b}^{\mathrm{2}} }{{c}+{a}}\:+\frac{{c}^{\mathrm{2}} }{{a}+{b}}=\mathrm{0} \\ $$ Answered by ajfour last updated on 15/May/18 $$\frac{{a}}{{b}+{c}}+\frac{{b}}{{c}+{a}}+\frac{{c}}{{a}+{b}}=\mathrm{1}…