Question Number 145626 by mathdanisur last updated on 06/Jul/21 Commented by mr W last updated on 06/Jul/21 $$\mid{a}+{b}\mid\leqslant\mid{a}\mid+\mid{b}\mid \\ $$$$\frac{\mid{a}\mid+\mid{b}\mid}{\mid{a}+{b}\mid}\geqslant\mathrm{1} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mid{a}\mid+\mid{b}\mid}{\mid{a}+{b}\mid}\geqslant\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{1}=\frac{\mathrm{3}}{\mathrm{2}}={min} \\ $$ Commented…
Question Number 80084 by behi83417@gmail.com last updated on 30/Jan/20 $$\:\:−\mathrm{1}=\left(−\mathrm{1}\right)^{\mathrm{1}} =\left(−\mathrm{1}\right)^{\frac{\mathrm{2}}{\mathrm{2}}} =\left(\left(−\mathrm{1}\right)^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} =\left(\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} = \\ $$$$=\sqrt{\mathrm{1}}=\mathrm{1}\:\: \\ $$$$\mathrm{what}\:\mathrm{do}\:\mathrm{you}\:\mathrm{think}\:\mathrm{about}\:\mathrm{this}? \\ $$ Commented by key of…
Question Number 145615 by loveineq last updated on 06/Jul/21 $$\mathrm{Let}\:{a},{b},{c}\:>\:\mathrm{0}\:\mathrm{and}\:{abc}\:=\:\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\mathrm{3}} }{\left({a}+\mathrm{1}\right)^{\mathrm{2}} }+\frac{{b}^{\mathrm{3}} }{\left({b}+\mathrm{1}\right)^{\mathrm{2}} }+\frac{{c}^{\mathrm{3}} }{\left({c}+\mathrm{1}\right)^{\mathrm{2}} }\:\geqslant\frac{{a}+{b}+{c}}{\mathrm{4}}\:\:\:\:\:\:\:\:\:\:\:\: \\ $$ Commented by justtry last updated…
Question Number 80068 by Pratah last updated on 30/Jan/20 Commented by mr W last updated on 30/Jan/20 $${sir}\:{Pratah}: \\ $$$${are}\:{you}\:{student}?\:{teacher}?\:{professor}? \\ $$$${what}'{s}\:{the}\:{source}\:{of}\:{your}\:{questions}? \\ $$ Commented…
Question Number 14535 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 01/Jun/17 Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 01/Jun/17 $${hello}\:{dears}. \\ $$$${this}\:{is}\:{an}\:{ancient}\:{system}\:{of}\:{equiations} \\ $$$${that}\:{have}\:{not}\:{solved}\:{by}\:{any}\:{one}\:{yet}. \\ $$$${but}\:{i}\:{think}\:{by}\:{studing}\:{several}\:{ways} \\ $$$${that}\:{used}\:{for}\:{solveing}\:{Q}.\mathrm{14157},{now}\:…
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Question Number 80053 by mr W last updated on 30/Jan/20 $${Find}\:{integer}\:{x},\:{y}\:{such}\:{that} \\ $$$$\mathrm{2}^{{x}} −{y}^{\mathrm{2}} =\mathrm{615} \\ $$ Commented by john santu last updated on 30/Jan/20…
Question Number 145580 by mathdanisur last updated on 06/Jul/21 Commented by imjagoll last updated on 06/Jul/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 145577 by mathlove last updated on 06/Jul/21 Commented by mr W last updated on 06/Jul/21 $${see}\:{Q}\mathrm{145256} \\ $$ Answered by puissant last updated…
Question Number 80039 by jagoll last updated on 30/Jan/20 $${prove}\:{that} \\ $$$$\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\geqslant\mathrm{4} \\ $$ Commented by mr W last updated on 30/Jan/20 $${only}\:{for}\:{x}\in{R}^{+} \\ $$$$\mathrm{1}+{x}\geqslant\mathrm{2}\sqrt{{x}}…