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Author: Tinku Tara

Solve-the-equation-in-R-2-x-2-x-1-1-x-x-

Question Number 155153 by mathdanisur last updated on 26/Sep/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{in}\:\mathbb{R} \\ $$$$\sqrt{\mathrm{2}\left(\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{x}\:+\:\mathrm{1}\right)}\:=\:\mathrm{1}\:+\:\sqrt{\mathrm{x}}\:-\:\mathrm{x} \\ $$ Answered by MJS_new last updated on 26/Sep/21 $$\sqrt{{x}}\in\mathbb{R}\:\Rightarrow\:{x}\geqslant\mathrm{0}\:\mathrm{but}\:\mathrm{it}'\mathrm{s}\:\mathrm{easy}\:\mathrm{to}\:\mathrm{see}\:{x}\neq\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{lhs}>\mathrm{0}\:\Rightarrow\:\mathrm{1}+\sqrt{{x}}−{x}>\mathrm{0}…

Question-89618

Question Number 89618 by ajfour last updated on 18/Apr/20 Commented by ajfour last updated on 18/Apr/20 $${Find}\:{radii}\:{of}\:{the}\:{circles},\:{if} \\ $$$$\bigtriangleup{ABC}\:{is}\:{equilateral}\:{of}\:{side}\:{a}. \\ $$$$\left({E}\:{is}\:{the}\:{center}\:{of}\:{smaller}\:{circle}\right) \\ $$ Commented by…

let-n-N-solve-for-real-numbers-x-3n-y-2n-y-3n-x-2n-4-

Question Number 155154 by mathdanisur last updated on 26/Sep/21 $$\mathrm{let}\:\:\mathrm{n}\in\mathbb{N}^{+} \:\:\mathrm{solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{x}^{\mathrm{3}\boldsymbol{\mathrm{n}}} \:-\:\mathrm{y}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \:=\:\mathrm{y}^{\mathrm{3}\boldsymbol{\mathrm{n}}} \:-\:\mathrm{x}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \:=\:\mathrm{4} \\ $$ Answered by MJS_new last updated on…