m+(1/m)=5

Solution for m+(1/m)=5 equation:

m+(1/m)=5

We move all terms to the left:

m+(1/m)-(5)=0


Domain of the equation: m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

m+(+1/m)-5=0

We get rid of parentheses

m+1/m-5=0

We multiply all the terms by the denominator


m*m-5*m+1=0

We add all the numbers together, and all the variables

-5m+m*m+1=0

Wy multiply elements

m^2-5m+1=0

a = 1; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·1·1
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{21}}{2*1}=\frac{5-\sqrt{21}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{21}}{2*1}=\frac{5+\sqrt{21}}{2}
$