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Question-46395




Question Number 46395 by Meritguide1234 last updated on 25/Oct/18
Answered by MJS last updated on 25/Oct/18
x=(√5)−(1/(1+(1/(1+(1/(1+(1/(1+(1/(1+(1/x)))))))))))  x=(√5)−((5x+3)/(8x+5))  x^2 +((5−4(√5))/4)x+((3−5(√5))/8)=0  x_1 =−(7/4)+((√5)/2)  x_2 =(1/2)+((√5)/2)
$${x}=\sqrt{\mathrm{5}}−\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{{x}}}}}}} \\ $$$${x}=\sqrt{\mathrm{5}}−\frac{\mathrm{5}{x}+\mathrm{3}}{\mathrm{8}{x}+\mathrm{5}} \\ $$$${x}^{\mathrm{2}} +\frac{\mathrm{5}−\mathrm{4}\sqrt{\mathrm{5}}}{\mathrm{4}}{x}+\frac{\mathrm{3}−\mathrm{5}\sqrt{\mathrm{5}}}{\mathrm{8}}=\mathrm{0} \\ $$$${x}_{\mathrm{1}} =−\frac{\mathrm{7}}{\mathrm{4}}+\frac{\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$${x}_{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$
Commented by Meritguide1234 last updated on 25/Oct/18
nice solution
$${nice}\:{solution} \\ $$

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