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Category: Algebra

Question-119059

Question Number 119059 by qqqqqqqqq last updated on 21/Oct/20 Answered by MJS_new last updated on 21/Oct/20 $$\sqrt{{x}^{\mathrm{2}} +{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)^{\mathrm{2}} +\left({x}+\mathrm{1}\right)^{\mathrm{2}} }−{x}^{\mathrm{2}} = \\ $$$$=\sqrt{{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{3}}…

Question-119052

Question Number 119052 by shahria14 last updated on 21/Oct/20 Answered by 1549442205PVT last updated on 22/Oct/20 $$\mid\mathrm{x}^{\mathrm{2}} −\mathrm{1}\mid\leqslant\mathrm{3}\Leftrightarrow−\mathrm{3}\leqslant\mathrm{x}^{\mathrm{2}} −\mathrm{1}\leqslant\mathrm{3}\Leftrightarrow−\mathrm{2}\leqslant\mathrm{x}^{\mathrm{2}} \leqslant\mathrm{4} \\ $$$$\Leftrightarrow\mathrm{x}^{\mathrm{2}} \leqslant\mathrm{4}\Leftrightarrow\mid\mathrm{x}\mid\leqslant\mathrm{2}\Leftrightarrow−\mathrm{2}\leqslant\mathrm{x}\leqslant\mathrm{2} \\ $$$$…

Show-by-recurence-that-n-N-k-1-n-1-k-k-1-k-2-n-n-3-4-n-1-n-2-

Question Number 119055 by mathocean1 last updated on 21/Oct/20 $$ \\ $$$${Show}\:{by}\:{recurence}\:{that}:\:\forall\:{n}\in\mathbb{N}^{\ast} \\ $$$$\sum_{{k}=\mathrm{1}} ^{{n}} \frac{\mathrm{1}}{{k}\left({k}+\mathrm{1}\right)\left({k}+\mathrm{2}\right)}=\frac{{n}\left({n}+\mathrm{3}\right)}{\mathrm{4}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)} \\ $$ Answered by Bird last updated on 21/Oct/20…

1-x-x-2-2a-1-x-x-1-0-solve-for-x-

Question Number 53491 by ajfour last updated on 22/Jan/19 $$\left(\frac{\mathrm{1}+{x}}{\:\sqrt{{x}}}\right)^{\mathrm{2}} +\mathrm{2}{a}\left(\frac{\mathrm{1}+{x}}{\:\sqrt{{x}}}\right)+\mathrm{1}=\mathrm{0} \\ $$$${solve}\:{for}\:{x}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 22/Jan/19 $${k}^{\mathrm{2}} +\mathrm{2}{ak}+{a}^{\mathrm{2}} +\mathrm{1}={a}^{\mathrm{2}}…

Suppose-that-the-sum-of-the-square-of-complex-numbers-x-or-y-is-7-and-the-sum-of-their-cubes-is-10-Find-the-largest-true-value-of-the-sum-x-y-that-satisfies-these-conditions-A-4-B-5-C-6-D

Question Number 184555 by Shrinava last updated on 08/Jan/23 $$\mathrm{Suppose}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of} \\ $$$$\mathrm{complex}\:\mathrm{numbers}\:\:\boldsymbol{\mathrm{x}}\:\mathrm{or}\:\boldsymbol{\mathrm{y}}\:\mathrm{is}\:\mathrm{7}\:,\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{cubes}\:\mathrm{is}\:\mathrm{10}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{largest} \\ $$$$\mathrm{true}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sum}\:\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\:\:\mathrm{that}\:\mathrm{satisfies} \\ $$$$\mathrm{these}\:\mathrm{conditions}. \\ $$$$\left.\mathrm{A}\left.\right)\left.\mathrm{4}\left.\:\left.\:\:\mathrm{B}\right)\mathrm{5}\:\:\:\mathrm{C}\right)\mathrm{6}\:\:\:\mathrm{D}\right)\mathrm{7}\:\:\:\mathrm{E}\right)\mathrm{8} \\ $$ Commented by mr…

Resoudre-dans-Z-x-y-xy-39-

Question Number 184551 by a.lgnaoui last updated on 08/Jan/23 $${Resoudre}\:{dans}\:\mathbb{Z}^{+} \\ $$$${x}+{y}+\sqrt{{xy}}\:\:\:\:=\mathrm{39} \\ $$ Answered by Frix last updated on 08/Jan/23 $${xy}\geqslant\mathrm{0}\:\Rightarrow\:{x}\geqslant\mathrm{0}\wedge{y}\geqslant\mathrm{0}\vee{x}<\mathrm{0}\wedge{y}<\mathrm{0} \\ $$$$\left(\mathrm{1}\right)\:{x}<\mathrm{0}\wedge{y}<\mathrm{0} \\…