X-1/x=1=x^2

Solution for X-1/x=1=x^2 equation:

X-1/X=1=X^2

We move all terms to the left:

X-1/X-(1)=0


Domain of the equation: X!=0

X∈R


We multiply all the terms by the denominator


X*X-1*X-1=0

We add all the numbers together, and all the variables

-1X+X*X-1=0

Wy multiply elements

X^2-1X-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:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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