(1+y)=1/y

Solution for (1+y)=1/y equation:

(1+y)=1/y

We move all terms to the left:

(1+y)-(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)-(+1/y)=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

y+y*y-1=0

Wy multiply elements

y^2+y-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}
$