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Category: Algebra

Let-a-b-x-y-gt-0-and-a-x-b-y-a-b-2-Prove-that-a-y-x-b-x-y-b-x-a-a-y-b-

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-10694

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}…

f-x-5x-1-4-f-a-f-b-9-2-a-b-

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}} \\…

f-x-y-f-x-f-y-f-16-8-f-64-

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) \\…

x-2-2x-9-9-x-1-2-0-please-

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}}…

x-2-y-y-2-5-xy-x-1-y-2-xy-2-2-x-y-Find-x-y-

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}…

1-64-5-3-1-3-

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}}}…