Question Number 78340 by loveineq. last updated on 16/Jan/20 $$\mathrm{Let}\:\:{a},{b},{c}\:>\:\mathrm{0}\:\:\mathrm{and}\:\:{c}^{\mathrm{2}} \:=\:\frac{{ab}+{bc}+{ca}}{\mathrm{3}}\:.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\mathrm{3}} +{b}^{\mathrm{3}} −\mathrm{2}{c}^{\mathrm{3}} }{{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} }\:\leqslant\:\mathrm{3}\left(\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −\mathrm{2}{c}^{\mathrm{2}} }{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }\right)…
Question Number 143875 by ajfour last updated on 19/Jun/21 Commented by ajfour last updated on 19/Jun/21 $${solve}\:{for}\:{m}\:{in}\:{terms}\:{of} \\ $$$${a},{b},{c},{d}. \\ $$ Terms of Service Privacy…
Question Number 78335 by john santu last updated on 16/Jan/20 $${find}\:{the}\:{solution}\:{of} \\ $$$$\frac{{x}}{\left({x}−\mathrm{2}\right)^{\mathrm{3}} +\left({x}−\mathrm{3}\right)^{\mathrm{3}} −\mathrm{1}}\:\geqslant\:\mathrm{0} \\ $$ Answered by MJS last updated on 16/Jan/20 $$\Rightarrow\:{x}>\mathrm{0}\wedge\left(\left({x}−\mathrm{2}\right)^{\mathrm{3}}…
Question Number 12797 by tawa last updated on 01/May/17 $$\mathrm{1}\:+\:\mathrm{x}\:+\:\mathrm{x}^{\mathrm{2}} \:+\:…\:\mathrm{x}^{\mathrm{49}} \:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{x}^{\mathrm{49}} \:−\:\frac{\mathrm{1}}{\mathrm{x}}\right) \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$ Commented by prakash jain last updated on 01/May/17…
Question Number 78319 by clarissagirl last updated on 16/Jan/20 $$\mathrm{57}+\mathrm{6}{h}=\mathrm{16}{h}−\mathrm{33} \\ $$ Commented by jagoll last updated on 16/Jan/20 $$\mathrm{10}{h}=\mathrm{90}\:\Rightarrow\:{h}=\mathrm{9} \\ $$ Terms of Service…
Question Number 78306 by mathocean1 last updated on 15/Jan/20 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{age}\:\mathrm{of}\:\mathrm{Hamadou}\:\:\: \\ $$$$\mathrm{his}\:\mathrm{wife}\:\mathrm{and}\:\mathrm{theirs}\:\mathrm{son}\:\mathrm{is}\:\mathrm{100}. \\ $$$$\mathrm{n}\:\mathrm{years}\:\mathrm{ago}\:\mathrm{the}\:\mathrm{wife}\:\mathrm{had}\:\mathrm{the}\: \\ $$$$\mathrm{quadruple}\:\mathrm{of}\:\mathrm{his}\:\mathrm{son}'\mathrm{s}\:\mathrm{age}\:\mathrm{and}\: \\ $$$$\mathrm{Hamadou}\:\mathrm{was}\:\mathrm{6}\:\mathrm{time}\:\mathrm{older}\:\mathrm{than} \\ $$$$\mathrm{his}\:\mathrm{son}. \\ $$$$\mathrm{Determine}\:\mathrm{theirs}\:\mathrm{ages}. \\ $$$$ \\…
Question Number 143832 by mathdanisur last updated on 18/Jun/21 $${x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:=\:\left(\frac{\mathrm{56}}{\mathrm{13}}\right)^{\mathrm{2}} \:{and}\:\:{x}\:+\:\frac{\mathrm{5}{y}}{\mathrm{12}}\:=\:\frac{\mathrm{56}}{\mathrm{12}} \\ $$$${find}\:\:{x}+{y}=? \\ $$ Answered by MJS_new last updated on 18/Jun/21 $${x}^{\mathrm{2}}…
Solve-simultaneously-2x-y-z-8-equation-i-x-2-y-2-2z-2-14-equation-ii-3x-3-4y-3-z-3-195-equation-iii-
Question Number 12763 by tawa last updated on 30/Apr/17 $$\mathrm{Solve}\:\mathrm{simultaneously} \\ $$$$\mathrm{2x}\:+\:\mathrm{y}\:−\:\mathrm{z}\:=\:\mathrm{8}\:\:\:\:\:\:\:\:………..\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{2z}^{\mathrm{2}} \:=\:\mathrm{14}\:\:\:\:\:\:\:……….\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$$$\mathrm{3x}^{\mathrm{3}} \:+\:\mathrm{4y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \:=\:\mathrm{195}\:\:\:\:\:\:\:\:\:………..\:\mathrm{equation}\:\left(\mathrm{iii}\right) \\ $$ Terms…
Question Number 143822 by ajfour last updated on 18/Jun/21 $$\:{x}^{\mathrm{4}} +{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$${let}\:\:{x}=\frac{{t}}{{s}} \\ $$$$\Rightarrow\:{t}^{\mathrm{4}} +{as}^{\mathrm{2}} {t}^{\mathrm{2}} +{bs}^{\mathrm{3}} {t}+{cs}^{\mathrm{4}} =\mathrm{0} \\ $$$${let}\:{t}={p}+{h}\:\:\Rightarrow \\ $$$${p}^{\mathrm{4}}…
Question Number 143814 by mathdanisur last updated on 18/Jun/21 $$\forall{a};{b};{c}\in\mathbb{R}\:,\:{find}\:{all}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:,\:{such}\:{that} \\ $$$${f}\left({a}\right){f}\left({bc}\right)+\mathrm{9}\leqslant{f}\left({ab}\right)+\mathrm{5}{f}\left({ac}\right) \\ $$ Answered by Olaf_Thorendsen last updated on 18/Jun/21 $${f}\left({a}\right){f}\left({bc}\right)+\mathrm{9}\:\leqslant\:{f}\left({ab}\right)+\mathrm{5}{f}\left({ac}\right) \\ $$$$ \\…