X+(1/x)=2.05

Solution for X+(1/x)=2.05 equation:

X+(1/X)=2.05

We move all terms to the left:

X+(1/X)-(2.05)=0


Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X+(+1/X)-(2.05)=0

We add all the numbers together, and all the variables

X+(+1/X)-2.05=0

We get rid of parentheses

X+1/X-2.05=0

We multiply all the terms by the denominator


X*X-(2.05)*X+1=0

We multiply parentheses

X*X-2.05X+1=0

Wy multiply elements

X^2-2.05X+1=0

a = 1; b = -2.05; c = +1;
Δ = b2-4ac
Δ = -2.052-4·1·1
Δ = 0.2025
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{-(-2.05)-\sqrt{0.2025}}{2*1}=\frac{2.05-\sqrt{0.2025}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.05)+\sqrt{0.2025}}{2*1}=\frac{2.05+\sqrt{0.2025}}{2}
$