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Category: Algebra

Question-187496

Question Number 187496 by mathlove last updated on 18/Feb/23 Commented by mr W last updated on 18/Feb/23 $${things}\:{like}\:\mid\frac{\overset{\rightarrow} {{A}}}{\overset{\rightarrow} {{B}}}\mid\:{don}'{t}\:{exist}!\: \\ $$$${if}\:{you}\:{mean}\:\frac{\mid\overset{\rightarrow} {{A}}\mid}{\mid\overset{\rightarrow} {{B}}\mid},\:{then}\:{you}\:{should} \\…

resoudre-equation-2x-3-4-5-2-7-

Question Number 121957 by mlj5 last updated on 13/Nov/20 $${resoudre}\:{equation}\mid−\mathrm{2}{x}−\sqrt{\mathrm{3}/}\mathrm{4}\mid=\mathrm{5}−\mathrm{2}\sqrt{\mathrm{7}} \\ $$ Commented by MJS_new last updated on 13/Nov/20 $$\mathrm{what}\:\mathrm{does}\:\left[…\right]\:\mathrm{mean}?\:\mathrm{usually}\:\mathrm{it}'\mathrm{s}\:\mathrm{the}\:\mathrm{greatest} \\ $$$$\mathrm{integer}\:\mathrm{function},\:\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{has}\:\mathrm{no}\:\mathrm{solution}:\:\left[…\right]\in\mathbb{Z}\:\mathrm{but}\:\mathrm{5}−\mathrm{2}\sqrt{\mathrm{7}}\notin\mathbb{Z} \\…

Calculate-the-sum-k-1-n-1-k-k-2-1-

Question Number 121950 by liberty last updated on 12/Nov/20 $$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{sum}\:\underset{\mathrm{k}\:=\:\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\:\sqrt{\mathrm{k}+\sqrt{\mathrm{k}^{\mathrm{2}} +\mathrm{1}}}}\:. \\ $$ Answered by bobhans last updated on 12/Nov/20 $${let}\:{a}\:=\:{k}\:+\:\sqrt{{k}^{\mathrm{2}} −\mathrm{1}}\:{and}\:{b}\:=\:{k}−\sqrt{{k}^{\mathrm{2}} +\mathrm{1}}\:…

Question-187476

Question Number 187476 by mnjuly1970 last updated on 17/Feb/23 Answered by anurup last updated on 18/Feb/23 $$\mathrm{If}\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{xy}−\mathrm{2}{y}^{\mathrm{2}} −\mathrm{5}\left(\mathrm{2}{x}−{y}\right)=\mathrm{0} \\ $$$${x}^{\mathrm{2}} −\mathrm{2}{xy}−\mathrm{3}{y}^{\mathrm{2}} +\mathrm{15}=\mathrm{0} \\ $$$$\mathrm{find}\:{x},{y}.…

let-a-and-b-be-positive-integers-such-that-ab-1-divides-a-2-b-2-show-that-a-2-b-2-ab-1-is-the-sequare-of-an-integer-

Question Number 187478 by normans last updated on 17/Feb/23 $$\: \\ $$$$\:\:\:\boldsymbol{{let}}\:\boldsymbol{{a}}\:\boldsymbol{{and}}\:\boldsymbol{{b}}\:\boldsymbol{{be}}\:\boldsymbol{{positive}}\:\boldsymbol{{integers}}\:\:\:\:\: \\ $$$$\:\:\:\boldsymbol{{such}}\:\boldsymbol{{that}}\:\boldsymbol{{ab}}\:+\:\mathrm{1}\:\boldsymbol{{divides}}\:\boldsymbol{{a}}^{\mathrm{2}} \:+\:\boldsymbol{{b}}^{\mathrm{2}} .\:\:\:\:\: \\ $$$$\:\:\:\:\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:\frac{\boldsymbol{{a}}^{\mathrm{2}} \:+\:\boldsymbol{{b}}^{\mathrm{2}} }{\boldsymbol{{ab}}\:+\:\mathrm{1}} \\ $$$$\:\:\:\:\:\:\boldsymbol{{is}}\:\boldsymbol{{the}}\:\boldsymbol{{sequare}}\:\boldsymbol{{of}}\:\boldsymbol{{an}}\:\boldsymbol{{integer}}. \\ $$$$ \\…

k-p-4-3-2-k-2-9-p-

Question Number 121919 by talminator2856791 last updated on 12/Nov/20 $$\: \\ $$$$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\underset{{k}={p}} {\overset{\infty} {\sum}}\:\mathrm{4}\centerdot\mathrm{3}^{\mathrm{2}−{k}} \:=\:\frac{\mathrm{2}}{\mathrm{9}} \\ $$$$\:\:\:\:\:\:\:\:\:\:{p}\:=\:? \\ $$$$\: \\ $$$$\:…

x-2-y-36-x-y-2-25-x-y-

Question Number 121913 by Jamshidbek2311 last updated on 12/Nov/20 $$\begin{cases}{{x}^{\mathrm{2}} +{y}=\mathrm{36}}\\{{x}+{y}^{\mathrm{2}} =\mathrm{25}\:\:{x}=?\:{y}=?}\end{cases} \\ $$ Answered by MJS_new last updated on 12/Nov/20 $$\left(\mathrm{1}\right)\:{y}=\mathrm{36}−{x}^{\mathrm{2}} \\ $$$$\Rightarrow \\…