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Category: Algebra

a-1-b-2-2-3-c-1-c-1-3-4-2a-c-10-

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-75618

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} \\…

x-6-y-4-z-k-k-x-y-z-25-k-

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-10078

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}}…

3a-4b-5c-2a-3b-c-146-c-

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}…

Find-the-smallest-value-5x-16-x-21-over-positive-value-of-x-

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} \\…

a-b-c-a-b-1-2-a-b-c-b-c-1-2-a-b-c-a-c-1-a-b-c-

Question Number 10067 by konen last updated on 22/Jan/17 $$\frac{\mathrm{a}×\mathrm{b}×\mathrm{c}}{\mathrm{a}+\mathrm{b}}=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\frac{\mathrm{a}×\mathrm{b}×\mathrm{c}}{\mathrm{b}+\mathrm{c}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\frac{\mathrm{a}×\mathrm{b}×\mathrm{c}}{\mathrm{a}+\mathrm{c}}=\mathrm{1} \\ $$$$\Rightarrow\mathrm{a}×\mathrm{b}×\mathrm{c}=? \\ $$$$ \\ $$$$ \\ $$ Answered by mrW1…