Menu Close

x-1-1-1-1-x-and-y-2-2-1-1-y-find-x-y-




Question Number 89920 by akash4081 last updated on 20/Apr/20
x=(1/(1+(1/(1+x)))) and y=(2/(2+(1/(1+y )))) find x+y
$${x}=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+{x}}}\:{and}\:{y}=\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{1}+{y}\:}}\:{find}\:{x}+{y} \\ $$
Commented by john santu last updated on 20/Apr/20
x = ((x+1)/(x+2)) ⇒ x = ((−1 ± (√5))/2)  y = ((2(y+1))/(2y+3)) ⇒ y = ((−1 ± (√(17)))/4)  ∴ x+y = (((−1±(√5))/2))+(((−1±(√(17)))/4))
$${x}\:=\:\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}\:\Rightarrow\:{x}\:=\:\frac{−\mathrm{1}\:\pm\:\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$${y}\:=\:\frac{\mathrm{2}\left({y}+\mathrm{1}\right)}{\mathrm{2}{y}+\mathrm{3}}\:\Rightarrow\:{y}\:=\:\frac{−\mathrm{1}\:\pm\:\sqrt{\mathrm{17}}}{\mathrm{4}} \\ $$$$\therefore\:{x}+{y}\:=\:\left(\frac{−\mathrm{1}\pm\sqrt{\mathrm{5}}}{\mathrm{2}}\right)+\left(\frac{−\mathrm{1}\pm\sqrt{\mathrm{17}}}{\mathrm{4}}\right) \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *