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Category: Algebra

Question-145626

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…

1-1-1-1-2-2-1-2-1-2-1-1-2-1-1-what-do-you-think-about-this-

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…

Let-a-b-c-gt-0-and-abc-1-Prove-that-a-3-a-1-2-b-3-b-1-2-c-3-c-1-2-a-b-c-4-

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-14535

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}\:…