a+1/a=9

Solution for a+1/a=9 equation:

a+1/a=9

We move all terms to the left:

a+1/a-(9)=0


Domain of the equation: a!=0

a∈R


We multiply all the terms by the denominator


a*a-9*a+1=0

We add all the numbers together, and all the variables

-9a+a*a+1=0

Wy multiply elements

a^2-9a+1=0

a = 1; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·1·1
Δ = 77
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{77}}{2*1}=\frac{9-\sqrt{77}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{77}}{2*1}=\frac{9+\sqrt{77}}{2}
$