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Question Number 81980 by Hassen_Timol last updated on 17/Feb/20

Commented by Hassen_Timol last updated on 17/Feb/20

$$\mathrm{What}\mathrm{are}\mathrm{the}\mathrm{values}\mathrm{of}\mathrm{these}2\mathrm{numbers}\mathrm{please}?$$

Commented by Hassen_Timol last updated on 17/Feb/20

$$\mathrm{May}\mathrm{you}\mathrm{give}\mathrm{a}\mathrm{proof}\mathrm{for}\mathrm{it},\mathrm{please}?$$

Answered by $@ty@m123 last updated on 17/Feb/20

$$x=\frac{1}{1+x}$$$$x^2+x-1=0$$$$x=\frac{-1\pm \sqrt{1+4}}{2}$$$$x=\frac{-1+\sqrt{5}}{2}...\left(1\right)$$$$y=\sqrt{1+y}$$$$y^2-y-1=0$$$$y=\frac{1\pm \sqrt{1+4}}{2}=\frac{1\pm \sqrt{5}}{2}$$

Commented by mr W last updated on 17/Feb/20

$$y>0,thereforey=\frac{1+\sqrt{5}}{2}only.$$

Commented by Hassen_Timol last updated on 17/Feb/20

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}!!!$$

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