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Category: Algebra

x-y-z-R-If-1-x-1-y-z-1-2-1-y-1-x-z-1-3-1-z-1-x-y-1-4-x-y-z-

Question Number 183668 by mnjuly1970 last updated on 28/Dec/22 $$ \\ $$$$\:\:\:\:\:\:{x}\:,\:{y}\:,\:{z}\:\in\mathbb{R}: \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\mathrm{If}\:\:\:\:\begin{cases}{\frac{\mathrm{1}}{{x}}\:+\frac{\mathrm{1}}{{y}+{z}}\:=\frac{\mathrm{1}}{\mathrm{2}}}\\{\frac{\mathrm{1}}{{y}}\:+\frac{\mathrm{1}}{{x}+{z}}\:=\:\frac{\mathrm{1}}{\mathrm{3}}}\\{\frac{\mathrm{1}}{{z}_{\:} }\:+\frac{\mathrm{1}}{{x}+{y}}\:=\frac{\mathrm{1}}{\mathrm{4}}}\end{cases} \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\:\:\:{x}\:,\:{y}\:,\:{z}\:=? \\ $$$$ \\ $$ Commented by…

x-y-y-z-z-x-3-y-x-z-y-x-z-3-xyz-1-

Question Number 183592 by greougoury555 last updated on 27/Dec/22 $$\:\:\:\:\:\begin{cases}{\sqrt{\frac{{x}}{{y}}}\:+\sqrt{\frac{{y}}{{z}}}\:+\sqrt{\frac{{z}}{{x}}}\:=\:\mathrm{3}}\\{\sqrt{\frac{{y}}{{x}}}\:+\sqrt{\frac{{z}}{{y}}}\:+\sqrt{\frac{{x}}{{z}}}\:=\:\mathrm{3}}\\{\sqrt{{xyz}}\:=\:\mathrm{1}}\end{cases} \\ $$$$\: \\ $$$$ \\ $$ Answered by mr W last updated on 27/Dec/22 $${a}=\sqrt{\frac{{x}}{{y}}},\:{b}=\sqrt{\frac{{y}}{{z}}},\:{c}=\sqrt{\frac{{z}}{{x}}}…

Question-183556

Question Number 183556 by Shrinava last updated on 26/Dec/22 Answered by Frix last updated on 26/Dec/22 $${f}^{−\mathrm{1}} \left({x}\right)=\frac{{bx}+\mathrm{8}}{\left({a}−\mathrm{2}{b}\right){x}+{a}+\mathrm{2}} \\ $$$${f}^{−\mathrm{1}} \left(\mathrm{8}\right)=\frac{\mathrm{8}\left({b}+\mathrm{1}\right)}{\mathrm{9}{a}−\mathrm{2}\left(\mathrm{8}{b}−\mathrm{1}\right)} \\ $$ Terms of…