Question Number 76246 by benjo last updated on 25/Dec/19 $$\mathrm{how}\:\mathrm{to}\:\mathrm{solving}\:\mathrm{x}^{\mathrm{3}} \:+\mathrm{y}^{\mathrm{3}\:} \:=\mathrm{4}\:\mathrm{and}\: \\ $$$$\mathrm{x}×\mathrm{y}\:=\mathrm{1}? \\ $$ Answered by john santuy last updated on 25/Dec/19 $${let}\:{u}\:={x}^{\mathrm{3}\:}…
Question Number 141781 by gsk2684 last updated on 23/May/21 $${help}\:{me}\:{to}\:{find}\:{the}\:{roots}\:{of}\: \\ $$$${x}^{\mathrm{5}} +\mathrm{5}{x}^{\mathrm{4}} +\mathrm{20}{x}^{\mathrm{3}} +\mathrm{60}{x}^{\mathrm{2}} +\mathrm{120}{x}+\mathrm{120}=\mathrm{0}? \\ $$ Commented by MJS_new last updated on 23/May/21…
Question Number 141768 by loveineq last updated on 23/May/21 $$\mathrm{Let}\:{a},{b},{x},{y}\:>\:\mathrm{0}\:\mathrm{and}\:\left({a}+{x}\right)\left({b}+{y}\right)\:=\:\left({a}+{b}\right)^{\mathrm{2}} \:.\:\:\:\:\:\:\:\: \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}−{y}}{{x}}+\frac{{b}−{x}}{{y}}\:\leqslant\:\frac{{b}−{x}}{{a}}+\frac{{a}−{y}}{{b}}\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 10694 by ABD last updated on 23/Feb/17 Answered by mrW1 last updated on 23/Feb/17 $${f}\left(\mathrm{3}{x}^{\mathrm{4}} +{x}^{\mathrm{3}} \right)=\mathrm{6}{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{3}} −\mathrm{3}=\mathrm{2}\left(\mathrm{3}{x}^{\mathrm{4}} +{x}^{\mathrm{3}} \right)−\mathrm{3} \\ $$$$\Rightarrow{f}\left({x}\right)=\mathrm{2}{x}−\mathrm{3}…
Question Number 10693 by ABD last updated on 23/Feb/17 $${f}\left({x}\right)=\frac{\mathrm{5}{x}−\mathrm{1}}{\mathrm{4}}\:\:,\:{f}\left({a}\right)+{f}\left({b}\right)=\frac{\mathrm{9}}{\mathrm{2}} \\ $$$$\Rightarrow{a}+{b}=? \\ $$ Answered by nume1114 last updated on 23/Feb/17 $${f}\left({x}\right)=\frac{\mathrm{5}{x}−\mathrm{1}}{\mathrm{4}} \\ $$$$\Rightarrow{f}\left({a}\right)=\frac{\mathrm{5}{a}−\mathrm{1}}{\mathrm{4}},{f}\left({b}\right)=\frac{\mathrm{5}{b}−\mathrm{1}}{\mathrm{4}} \\…
Question Number 10692 by ABD last updated on 23/Feb/17 $${f}\left({x}+{y}\right)={f}\left({x}\right)×{f}\left({y}\right) \\ $$$${f}\left(\mathrm{16}\right)=\mathrm{8}\:\Rightarrow{f}\left(\mathrm{64}\right) \\ $$ Answered by nume1114 last updated on 23/Feb/17 $${f}\left(\mathrm{64}\right)={f}\left(\left(\mathrm{16}+\mathrm{16}\right)+\left(\mathrm{16}+\mathrm{16}\right)\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:={f}\left(\mathrm{16}+\mathrm{16}\right)×{f}\left(\mathrm{16}+\mathrm{16}\right) \\…
Question Number 141753 by mohammad17 last updated on 23/May/21 $$\int\frac{{dx}}{{sinx}+{cosx}} \\ $$ Commented by mohammad17 last updated on 23/May/21 $${help}\:{me}\:{sir} \\ $$ Answered by rs4089…
Question Number 76214 by Emmanuel_N last updated on 25/Dec/19 $$\mathrm{x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{9}+\frac{\mathrm{9}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }=\mathrm{0} \\ $$$$\mathrm{please} \\ $$ Answered by benjo last updated on 25/Dec/19 $$\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \:−\mathrm{10}+\mathrm{9}/\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}}…
Question Number 141749 by Huy last updated on 23/May/21 $$\begin{cases}{\mathrm{x}^{\mathrm{2}} −\mathrm{y}+\sqrt{\mathrm{y}^{\mathrm{2}} +\mathrm{5}}=\mathrm{xy}−\sqrt{\mathrm{x}−\mathrm{1}}}\\{\mathrm{y}^{\mathrm{2}} +\sqrt{\mathrm{xy}+\mathrm{2}}=\mathrm{2}\left(\mathrm{x}+\mathrm{y}\right)}\end{cases} \\ $$$$\mathrm{Find}\:\mathrm{x},\mathrm{y} \\ $$ Answered by MJS_new last updated on 23/May/21 $$\mathrm{assuming}\:\mathrm{a}\:“\mathrm{nice}''\:\mathrm{solution}\:\mathrm{I}\:\mathrm{tried}…
Question Number 76213 by Emmanuel_N last updated on 25/Dec/19 $$\left(\frac{\mathrm{1}}{\mathrm{64}}×\mathrm{5}^{−\mathrm{3}} \right)^{−\frac{\mathrm{1}}{\mathrm{3}}} \\ $$ Answered by MJS last updated on 25/Dec/19 $$=\left(\mathrm{4}^{−\mathrm{3}} ×\mathrm{5}^{−\mathrm{3}} \right)^{−\frac{\mathrm{1}}{\mathrm{3}}} =\left(\mathrm{20}^{−\mathrm{3}} \right)^{−\frac{\mathrm{1}}{\mathrm{3}}}…