Question Number 211377 by jacklau last updated on 07/Sep/24 $$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{irrational}}\:\boldsymbol{\mathrm{number}}\: \\ $$$$\:^{\mathrm{3}} \sqrt{\:^{\mathrm{3}} \sqrt{\mathrm{2}}−\mathrm{1}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{written}}\:\boldsymbol{\mathrm{as}}\:^{\mathrm{3}} \sqrt{\boldsymbol{\mathrm{p}}}\:+\:^{\mathrm{3}} \sqrt{\boldsymbol{\mathrm{q}}}\:+\:^{\mathrm{3}} \sqrt{\boldsymbol{\mathrm{r}}}\: \\ $$$$\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{p}},\:\boldsymbol{\mathrm{q}},\:\boldsymbol{\mathrm{r}}\:? \\ $$ Terms of Service Privacy…
Question Number 211330 by RojaTaniya last updated on 06/Sep/24 Answered by mr W last updated on 06/Sep/24 $${say}\:{p}=\frac{{a}}{{b}},\:{q}=\frac{{b}}{{c}},\:{r}=\frac{{c}}{{a}} \\ $$$${pqr}=\mathrm{1} \\ $$$${p}+{q}+{r}=\mathrm{7} \\ $$$$\frac{\mathrm{1}}{{p}}+\frac{\mathrm{1}}{{q}}+\frac{\mathrm{1}}{{r}}=\mathrm{11}\: \\…
Question Number 211331 by efronzo1 last updated on 06/Sep/24 $$\:\:\:\:\:\mathrm{x}=\frac{\sqrt{\mathrm{6}}+\mathrm{2}+\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{6}}+\sqrt{\mathrm{3}}−\mathrm{2}−\sqrt{\mathrm{2}}} \\ $$$$\:\:\:\:\mathrm{y}=\frac{\sqrt{\mathrm{6}}−\sqrt{\mathrm{3}}−\mathrm{2}+\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{6}}−\sqrt{\mathrm{3}}+\mathrm{2}−\sqrt{\mathrm{2}}} \\ $$$$\:\:\:\mathrm{x}^{\mathrm{5}} −\mathrm{y}^{\mathrm{5}} \:=?\: \\ $$ Answered by A5T last updated on 06/Sep/24…
Question Number 211310 by hardmath last updated on 05/Sep/24 $$\mathrm{Find}: \\ $$$$\mathrm{LCD}\left(\mathrm{2}^{\mathrm{100}} \:−\:\mathrm{1}\:\:;\:\:\mathrm{2}^{\mathrm{120}} \:−\:\mathrm{1}\right)\:=\:? \\ $$ Answered by A5T last updated on 05/Sep/24 $${What}\:{is}\:{LCD}?\:{Do}\:{you}\:{mean}\:{GCD}\:{or}\:{LCM}? \\…
Question Number 211311 by a.lgnaoui last updated on 05/Sep/24 $$\boldsymbol{\mathrm{Dterminer}}\:\boldsymbol{\mathrm{le}}\:\boldsymbol{\mathrm{nombre}}\:\boldsymbol{\mathrm{total}}\:\:\boldsymbol{\mathrm{des}}\:\boldsymbol{\mathrm{nombres}}\: \\ $$$$\boldsymbol{\mathrm{de}}\:\left(\mathrm{3}\:\boldsymbol{\mathrm{chiffres}}\right)\boldsymbol{\mathrm{qui}}\:\boldsymbol{\mathrm{sont}}\:\boldsymbol{\mathrm{impair}}\left(\:\boldsymbol{\mathrm{et}}\right)\:\boldsymbol{\mathrm{divisibles}}\: \\ $$$$\boldsymbol{\mathrm{par}}\:\mathrm{9}\:\:\:\boldsymbol{\mathrm{compris}}\:\boldsymbol{\mathrm{entre}}\:\mathrm{100}\:\boldsymbol{\mathrm{et}}\:\mathrm{500}.? \\ $$$$\boldsymbol{\mathrm{formule}}\:\boldsymbol{\mathrm{si}}\:\boldsymbol{\mathrm{c}}\:\boldsymbol{\mathrm{est}}\:\boldsymbol{\mathrm{possible}}? \\ $$$$ \\ $$ Answered by mr W last…
Question Number 211262 by mathlove last updated on 03/Sep/24 Answered by mahdipoor last updated on 03/Sep/24 $${f}\left({m}\right)+{f}\left(\mathrm{1}−{m}\right)=\frac{{a}^{{m}−\mathrm{1}} \:}{{a}^{{m}} +{b}}+\frac{{a}^{−{m}} }{{a}^{\mathrm{1}−{m}} +{b}}= \\ $$$$\frac{{a}^{{m}−\mathrm{1}} \left({a}^{\mathrm{1}−{m}} +{b}\right)+{a}^{−{m}}…
Question Number 211255 by ajfour last updated on 02/Sep/24 $$\sqrt{{a}+\sqrt{{b}−{x}}+\sqrt{{b}−\sqrt{{a}+{x}}}}=\mathrm{2}{x} \\ $$$${solve}\:{for}\:{x}.\:\:\:\: \\ $$ Commented by Ghisom last updated on 03/Sep/24 $$\sqrt{{a}+\sqrt{{b}−{x}}+\sqrt{{b}−\sqrt{{a}+{x}}}}=\mathrm{2}{x} \\ $$$${x}=\left({b}−\left(\mathrm{4}{x}^{\mathrm{2}} −\sqrt{{b}−{x}}−{a}\right)^{\mathrm{2}}…
Question Number 211252 by RojaTaniya last updated on 02/Sep/24 Answered by Frix last updated on 02/Sep/24 $$\left[\mathrm{1}\right]×\left({x}−{y}\right)\:\Rightarrow\:{x}^{\mathrm{3}} −{y}^{\mathrm{3}} =\mathrm{39}\left({x}−{y}\right)\:\:\left[\mathrm{1}{a}\right] \\ $$$$\left[\mathrm{2}\right]×\left({y}−{z}\right)\:\Rightarrow\:{y}^{\mathrm{3}} −{z}^{\mathrm{3}} =\mathrm{49}\left({y}−{z}\right)\:\:\left[\mathrm{2}{a}\right] \\ $$$$\left[\mathrm{3}\right]×\left({z}−{x}\right)\:\Rightarrow\:{z}^{\mathrm{3}}…
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Question Number 211250 by RojaTaniya last updated on 01/Sep/24 $${Find}\:{the}\:{number}\:{of}\:\mathrm{4}\:{digit}\:{numbers} \\ $$$$\:{so}\:{that}\:{when}\:{decomposed}\:{into}\:{prime} \\ $$$$\:{factors},\:{have}\:{the}\:{sum}\:{of}\:{prime}\:{factors} \\ $$$$\:{equal}\:{to}\:{the}\:{sum}\:{of}\:{the}\:{exponents}? \\ $$ Answered by mr W last updated on…