x+1/x=11

Solution for x+1/x=11 equation:

x+1/x=11

We move all terms to the left:

x+1/x-(11)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-11*x+1=0

We add all the numbers together, and all the variables

-11x+x*x+1=0

Wy multiply elements

x^2-11x+1=0

a = 1; b = -11; c = +1;
Δ = b2-4ac
Δ = -112-4·1·1
Δ = 117
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3\sqrt{13}}{2*1}=\frac{11-3\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3\sqrt{13}}{2*1}=\frac{11+3\sqrt{13}}{2}
$