X+1/x=64

Solution for X+1/x=64 equation:

X+1/X=64

We move all terms to the left:

X+1/X-(64)=0


Domain of the equation: X!=0

X∈R


We multiply all the terms by the denominator


X*X-64*X+1=0

We add all the numbers together, and all the variables

-64X+X*X+1=0

Wy multiply elements

X^2-64X+1=0

a = 1; b = -64; c = +1;
Δ = b2-4ac
Δ = -642-4·1·1
Δ = 4092
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:

$\sqrt{\Delta}=\sqrt{4092}=\sqrt{4*1023}=\sqrt{4}*\sqrt{1023}=2\sqrt{1023}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-2\sqrt{1023}}{2*1}=\frac{64-2\sqrt{1023}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+2\sqrt{1023}}{2*1}=\frac{64+2\sqrt{1023}}{2}
$