Question Number 141164 by iloveisrael last updated on 16/May/21 $$\:\:\:\:{Find}\:{maximum}\:{value}\: \\ $$$$\:\:\:{of}\:{the}\:{product}\:{xy}\left(\mathrm{72}−\mathrm{3}{x}−\mathrm{4}{y}\right) \\ $$$$\:\:\:\:{for}\:{positive}\:{value}\:{of}\:{x}\:\&\:{y}. \\ $$ Commented by mitica last updated on 16/May/21 $${max}=\mathrm{1152}\:{for}\:{x}=\mathrm{8},{y}=\mathrm{6} \\…
Question Number 10091 by konen last updated on 23/Jan/17 $$\frac{\mathrm{a}−\mathrm{1}}{\mathrm{b}−\mathrm{2}}\:=\frac{\mathrm{2}}{\mathrm{3}}\:\:,\frac{\mathrm{c}+\mathrm{1}}{\mathrm{c}−\mathrm{1}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\Rightarrow\mathrm{2a}−\mathrm{c}+\mathrm{10}=? \\ $$ Answered by ridwan balatif last updated on 24/Jan/17 $$\frac{\mathrm{a}−\mathrm{1}}{\mathrm{b}−\mathrm{2}}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\mathrm{3}\left(\mathrm{a}−\mathrm{1}\right)=\mathrm{2}\left(\mathrm{b}−\mathrm{2}\right)…
Question Number 75618 by peter frank last updated on 13/Dec/19 Commented by mind is power last updated on 13/Dec/19 $$\mathrm{use}\:\mathrm{x}+\mathrm{y}\geqslant\mathrm{2}\sqrt{\mathrm{xy}} \\ $$$$\left(\mathrm{a}+\mathrm{b}\right)\geqslant\mathrm{2}\sqrt{\mathrm{ab}},\left(\mathrm{a}+\mathrm{c}\right)\geqslant\mathrm{2}\sqrt{\mathrm{ac}},\mathrm{c}+\mathrm{a}\geqslant\mathrm{2}\sqrt{\mathrm{ca}} \\ $$$$\Rightarrow\left(\mathrm{a}+\mathrm{b}\right)\left(\mathrm{b}+\mathrm{c}\right)\left(\mathrm{c}+\mathrm{a}\right)\geqslant\mathrm{2}\sqrt{\mathrm{ab}}.\mathrm{2}\sqrt{\mathrm{bc}}.\mathrm{2}\sqrt{\mathrm{ac}}=\mathrm{8abc} \\…
Question Number 141153 by iloveisrael last updated on 16/May/21 Answered by iloveisrael last updated on 16/May/21 Commented by SamuelAsaana last updated on 16/May/21 $${i}\:{donot}\:{underdtand}\:{sir}\:{please}\:{explain}\:{for}\:{for}\:{me} \\…
Question Number 10082 by konen last updated on 23/Jan/17 $$\frac{\mathrm{x}}{\mathrm{6}}=\frac{\mathrm{y}}{\mathrm{4}}=\frac{\mathrm{z}}{\mathrm{k}}=\mathrm{k} \\ $$$$\mathrm{x}+\mathrm{y}+\mathrm{z}=−\mathrm{25} \\ $$$$\mathrm{k}=? \\ $$ Commented by ridwan balatif last updated on 23/Jan/17 $$\mathrm{x}+\mathrm{y}+\mathrm{z}=−\mathrm{25}…
Question Number 75616 by mr W last updated on 13/Dec/19 $${A}_{\mathrm{1}} =\mathrm{2} \\ $$$${B}_{\mathrm{1}} =\mathrm{1} \\ $$$${A}_{{n}+\mathrm{1}} ={A}_{{n}} −\mathrm{8}{B}_{{n}} \\ $$$${B}_{{n}+\mathrm{1}} ={A}_{{n}} +\mathrm{7}{B}_{{n}} \\ $$$${find}\:{A}_{{n}}…
Question Number 10078 by ridwan balatif last updated on 23/Jan/17 Commented by ridwan balatif last updated on 23/Jan/17 $$\mathrm{x}_{\mathrm{1}} ^{\mathrm{2011}} +\mathrm{x}_{\mathrm{2}} ^{\mathrm{2011}} =\mathrm{A}\:\mathrm{and}\:\mathrm{x}_{\mathrm{1}} ^{\mathrm{2012}} +\mathrm{x}_{\mathrm{2}}…
Question Number 10076 by konen last updated on 23/Jan/17 $$\mathrm{3a}=\mathrm{4b}=\mathrm{5c} \\ $$$$\mathrm{2a}+\mathrm{3b}−\mathrm{c}=\mathrm{146} \\ $$$$\Rightarrow\mathrm{c}=? \\ $$ Answered by ridwan balatif last updated on 23/Jan/17 $$\mathrm{3a}=\mathrm{5c}\rightarrow\mathrm{a}=\frac{\mathrm{5}}{\mathrm{3}}\mathrm{c}…
Question Number 75602 by peter frank last updated on 13/Dec/19 $${If}\:\mathrm{2}{x}^{\mathrm{2}} −{mxy}+\mathrm{3}{y}^{\mathrm{2}} −\mathrm{5}{y}−\mathrm{2} \\ $$$${have}\:{two}\:{rational}\:{factor}\:{then} \\ $$$${find}\:\:\:{m} \\ $$ Answered by mr W last updated…
Question Number 141136 by bobhans last updated on 16/May/21 $$\:\:\:\:{Find}\:{the}\:{smallest}\:{value}\: \\ $$$$\:\:\:\:\mathrm{5}{x}\:+\:\frac{\mathrm{16}}{{x}}\:+\:\mathrm{21}\:{over}\:{positive}\: \\ $$$$\:\:\:{value}\:{of}\:{x}\: \\ $$ Answered by iloveisrael last updated on 16/May/21 $$\:\Rightarrow\:\mathrm{5}{x}\:\&\:\frac{\mathrm{16}}{{x}}\:{have}\:{a}\:{constant}\:{product} \\…