y=1+1/y

Solution for y=1+1/y equation:

y=1+1/y

We move all terms to the left:

y-(1+1/y)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

y-(1/y+1)=0

We get rid of parentheses

y-1/y-1=0

We multiply all the terms by the denominator


y*y-1*y-1=0

We add all the numbers together, and all the variables

-1y+y*y-1=0

Wy multiply elements

y^2-1y-1=0

a = 1; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·1·(-1)
Δ = 5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{5}}{2*1}=\frac{1-\sqrt{5}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{5}}{2*1}=\frac{1+\sqrt{5}}{2}
$