Question Number 107438 by lalitchand last updated on 10/Aug/20 Answered by mr W last updated on 10/Aug/20 $${x}\left(\frac{\mathrm{1}}{{n}+{p}}+\frac{\mathrm{1}}{{p}+{m}}+\frac{\mathrm{1}}{{m}+{n}}\right)=\mathrm{3}+\frac{{m}}{{n}+{p}}+\frac{{n}}{{p}+{m}}+\frac{{p}}{{m}+{n}} \\ $$$$\Rightarrow{x}=\frac{\mathrm{3}+\frac{{m}}{{n}+{p}}+\frac{{n}}{{p}+{m}}+\frac{{p}}{{m}+{n}}}{\frac{\mathrm{1}}{{n}+{p}}+\frac{\mathrm{1}}{{p}+{m}}+\frac{\mathrm{1}}{{m}+{n}}} \\ $$ Terms of Service…
Question Number 172956 by dragan91 last updated on 03/Jul/22 Commented by Shrinava last updated on 04/Jul/22 $$\mathrm{say}:\:\mathrm{m}=\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{2} \\ $$$$\mathrm{ab}+\mathrm{ac}+\mathrm{bc}=\frac{\mathrm{4}−\mathrm{n}^{\mathrm{2}} }{\mathrm{3}}\geqslant\mathrm{0} \\ $$$$\mathrm{k}=\mathrm{abc} \\ $$$$…\Leftrightarrow\mathrm{k}\leqslant\frac{\mathrm{2}\left(\mathrm{n}−\mathrm{2}\right)\left(\mathrm{n}+\mathrm{2}\right)}{\mathrm{25}+\mathrm{2n}^{\mathrm{2}} }…
Question Number 172948 by Mikenice last updated on 03/Jul/22 Commented by Rasheed.Sindhi last updated on 03/Jul/22 $$\left.{x}+{y}=\mathrm{5}\:\:\:\:\::\right) \\ $$ Commented by Shrinava last updated on…
Question Number 41879 by Tawa1 last updated on 14/Aug/18 $$\mathrm{If}\:\mathrm{a}\:\mathrm{fraction}\:\mathrm{is}\:\mathrm{added}\:\mathrm{to}\:\mathrm{its}\:\mathrm{denominator}\:,\:\:\mathrm{it}\:\mathrm{reduces}\:\mathrm{to}\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{and}\: \\ $$$$\mathrm{when}\:\mathrm{the}\:\mathrm{same}\:\mathrm{fraction}\:\mathrm{added}\:\mathrm{to}\:\mathrm{numerator},\:\mathrm{it}\:\mathrm{also}\:\mathrm{reduces}\:\mathrm{to}\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{fraction} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{square}\:\mathrm{root}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{result}\:\mathrm{of}\:\mathrm{the}\:\mathrm{fraction}\:\mathrm{is}\:\mathrm{less} \\ $$$$\mathrm{than}\:\mathrm{1} \\ $$$$ \\ $$ Answered by tanmay.chaudhury50@gmail.com…
Question Number 41877 by Tawa1 last updated on 14/Aug/18 $$\mathrm{The}\:\mathrm{tens}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{a}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{number}\:\mathrm{is}\:\mathrm{3}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{the}\:\mathrm{units}\:\mathrm{digit}. \\ $$$$\mathrm{When}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{are}\:\mathrm{reversed},\:\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{reduced}\:\mathrm{by}\:\mathrm{27}. \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:? \\ $$ Answered by MrW3 last updated on 14/Aug/18 $${let}'{s}\:{say}\:{the}\:{number}\:{is}\:{ab} \\…
Question Number 172947 by Mikenice last updated on 03/Jul/22 Answered by Rasheed.Sindhi last updated on 03/Jul/22 $$\mathrm{5}^{{x}−\mathrm{2}} =\frac{\mathrm{125}^{{x}−\mathrm{1}} }{\mathrm{5}^{{x}+\mathrm{2}} } \\ $$$$\mathrm{5}^{{x}−\mathrm{2}} \centerdot\mathrm{5}^{{x}+\mathrm{2}} =\left(\mathrm{5}^{\mathrm{3}} \right)^{{x}−\mathrm{1}}…
Question Number 41866 by Tawa1 last updated on 14/Aug/18 Answered by MJS last updated on 14/Aug/18 $${m}=\mathrm{4}{d} \\ $$$${b}={d}+\mathrm{6} \\ $$$${b}:{d}:{e}=\mathrm{5}:\mathrm{3}:\mathrm{2} \\ $$$${e}=\frac{\mathrm{2}}{\mathrm{3}}{d} \\ $$$$…
Question Number 41860 by SmNayon11 last updated on 14/Aug/18 $$\left(\mathrm{1},\mathrm{2},\mathrm{3},……..\mathrm{100}\right){are}\:{given}\:{number} \\ $$$${find}\:{the}\:{value}\:{of}\:\Sigma\left(\mathrm{1}×\mathrm{2}\right) \\ $$ Commented by MJS last updated on 14/Aug/18 $$\mathrm{sorry}\:\mathrm{but}\:“\Sigma\left(\mathrm{1}×\mathrm{2}\right)''\:\mathrm{isn}'\mathrm{t}\:\mathrm{proper}\:\mathrm{math}\:\mathrm{language} \\ $$$$\mathrm{what}\:\mathrm{does}\:\mathrm{it}\:\mathrm{mean}\:“\mathrm{sum}\:\mathrm{of}\:\mathrm{one}\:\mathrm{multiplicated}\:\mathrm{with}\:\mathrm{two}''? \\…
Question Number 172929 by pete last updated on 03/Jul/22 $$\mathrm{A}\:\mathrm{man}\:\mathrm{purchased}\:\mathrm{180}\:\mathrm{copies}\:\mathrm{of}\:\mathrm{a}\:\mathrm{book} \\ $$$$\mathrm{at}\:\$\mathrm{250}.\mathrm{00}\:\boldsymbol{\mathrm{each}}.\:\mathrm{He}\:\mathrm{sold}\:{y}\:\mathrm{copies}\:\mathrm{at}\:\$\mathrm{300}.\mathrm{00} \\ $$$$\mathrm{each}\:\mathrm{and}\:\mathrm{the}\:\mathrm{rest}\:\mathrm{at}\:\mathrm{a}\:\mathrm{discount}\:\mathrm{of}\:\mathrm{5}\:\mathrm{cents}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{dollar}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cost}\:\mathrm{price}.\:\mathrm{If}\:\mathrm{he}\:\mathrm{made}\:\mathrm{a}\:\mathrm{profit} \\ $$$$\mathrm{of}\:\$\mathrm{7},\mathrm{125}.\mathrm{00},\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{y}? \\ $$ Commented by Rasheed.Sindhi last updated…
Question Number 107385 by bemath last updated on 10/Aug/20 $$\:\:\:\:\:\iddots\mathcal{B}{e}\mathcal{M}{ath}\iddots \\ $$$${Given}\:\mathrm{6}{x}^{\mathrm{2}} −\mathrm{6}{px}+\mathrm{14}{p}−\mathrm{2}=\mathrm{0} \\ $$$${has}\:{the}\:{roots}\:{are}\:\:{u}\:\&\:{v}\:{where}\:{u},{v}\:\notin\mathbb{Z} \\ $$$${If}\:{u},{v}\:\geqslant\:\mathrm{1}\:,\:{then}\:{the}\:{value}\:{of}\:\mid{u}−{v}\mid\:. \\ $$$$\left({a}\right)\mathrm{14}\:\:\:\:\:\left({b}\right)\mathrm{15}\:\:\:\:\:\left({c}\right)\mathrm{16}\:\:\:\:\:\left({d}\right)\mathrm{17}\:\:\:\left({e}\right)\:\mathrm{18} \\ $$ Commented by Her_Majesty last…