Question Number 121996 by Anuragkar last updated on 13/Nov/20 $$\lfloor{x}\rfloor\:+\lfloor\mathrm{2}{x}\rfloor+\lfloor\mathrm{4}{x}\rfloor+\lfloor\mathrm{8}{x}\rfloor+\lfloor\mathrm{16}{x}\rfloor+\lfloor\mathrm{32}{x}\rfloor=\mathrm{123456} \\ $$$${find}\:{all}\:{values}\:{of}\:{x}\:{for}\:{which}\:{this}\:{relation}\:{holds}? \\ $$ Answered by prakash jain last updated on 13/Nov/20 $${x}={n}+{f} \\ $$$${n}\left(\mathrm{1}+\mathrm{2}+\mathrm{4}+…+\mathrm{32}\right)…
Question Number 187534 by pythagore last updated on 18/Feb/23 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 121973 by bemath last updated on 13/Nov/20 $$\:{solve}\:{this}\:{equation}\: \\ $$$$\:\begin{cases}{{xy}+{x}+{y}=\mathrm{19}}\\{{yz}\:+\:{y}+{z}\:=\:\mathrm{11}}\\{{z}+{x}+{zx}\:=\:\mathrm{14}}\end{cases} \\ $$ Commented by liberty last updated on 13/Nov/20 $$\rightarrow\:\mathrm{x}\left(\mathrm{y}+\mathrm{1}\right)=\mathrm{19}−\mathrm{y}\:\wedge\:\mathrm{z}\left(\mathrm{y}+\mathrm{1}\right)=\mathrm{11}−\mathrm{y} \\ $$$$\Rightarrow\begin{cases}{\mathrm{x}=\frac{\mathrm{19}−\mathrm{y}}{\mathrm{y}+\mathrm{1}}}\\{\mathrm{z}=\frac{\mathrm{11}−\mathrm{y}}{\mathrm{y}+\mathrm{1}}}\end{cases}\:\Leftrightarrow\:\mathrm{substitution}\:\mathrm{to}\:\mathrm{eq}\left(\mathrm{3}\right) \\…
Question Number 187496 by mathlove last updated on 18/Feb/23 Commented by mr W last updated on 18/Feb/23 $${things}\:{like}\:\mid\frac{\overset{\rightarrow} {{A}}}{\overset{\rightarrow} {{B}}}\mid\:{don}'{t}\:{exist}!\: \\ $$$${if}\:{you}\:{mean}\:\frac{\mid\overset{\rightarrow} {{A}}\mid}{\mid\overset{\rightarrow} {{B}}\mid},\:{then}\:{you}\:{should} \\…
Question Number 121957 by mlj5 last updated on 13/Nov/20 $${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} \\ $$$$\mathrm{integer}\:\mathrm{function},\:\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{has}\:\mathrm{no}\:\mathrm{solution}:\:\left[…\right]\in\mathbb{Z}\:\mathrm{but}\:\mathrm{5}−\mathrm{2}\sqrt{\mathrm{7}}\notin\mathbb{Z} \\…
Question Number 121950 by liberty last updated on 12/Nov/20 $$\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 Number 121948 by abdilah last updated on 12/Nov/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 187476 by mnjuly1970 last updated on 17/Feb/23 Answered by anurup last updated on 18/Feb/23 $$\mathrm{If}\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{xy}−\mathrm{2}{y}^{\mathrm{2}} −\mathrm{5}\left(\mathrm{2}{x}−{y}\right)=\mathrm{0} \\ $$$${x}^{\mathrm{2}} −\mathrm{2}{xy}−\mathrm{3}{y}^{\mathrm{2}} +\mathrm{15}=\mathrm{0} \\ $$$$\mathrm{find}\:{x},{y}.…
Question Number 187478 by normans last updated on 17/Feb/23 $$\: \\ $$$$\:\:\:\boldsymbol{{let}}\:\boldsymbol{{a}}\:\boldsymbol{{and}}\:\boldsymbol{{b}}\:\boldsymbol{{be}}\:\boldsymbol{{positive}}\:\boldsymbol{{integers}}\:\:\:\:\: \\ $$$$\:\:\:\boldsymbol{{such}}\:\boldsymbol{{that}}\:\boldsymbol{{ab}}\:+\:\mathrm{1}\:\boldsymbol{{divides}}\:\boldsymbol{{a}}^{\mathrm{2}} \:+\:\boldsymbol{{b}}^{\mathrm{2}} .\:\:\:\:\: \\ $$$$\:\:\:\:\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:\frac{\boldsymbol{{a}}^{\mathrm{2}} \:+\:\boldsymbol{{b}}^{\mathrm{2}} }{\boldsymbol{{ab}}\:+\:\mathrm{1}} \\ $$$$\:\:\:\:\:\:\boldsymbol{{is}}\:\boldsymbol{{the}}\:\boldsymbol{{sequare}}\:\boldsymbol{{of}}\:\boldsymbol{{an}}\:\boldsymbol{{integer}}. \\ $$$$ \\…
Question Number 56386 by Tawa1 last updated on 15/Mar/19 Terms of Service Privacy Policy Contact: info@tinkutara.com