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x+2/x=3

x+2/x=3 equation

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Numerical solution:

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The solution

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    2    
x + - = 3
    x
x+2x=3x + \frac{2}{x} = 3
Simplify
Detail solution
Given the equation:
x+2x=3x + \frac{2}{x} = 3
Multiply the equation sides by the denominators:
and x
we get:
x(x+2x)=3xx \left(x + \frac{2}{x}\right) = 3 x
x2+2=3xx^{2} + 2 = 3 x
Move right part of the equation to
left part with negative sign.

The equation is transformed from
x2+2=3xx^{2} + 2 = 3 x
to
x2−3x+2=0x^{2} - 3 x + 2 = 0
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=−3b = -3
c=2c = 2
, then
D = b^2 - 4 * a * c = 

(-3)^2 - 4 * (1) * (2) = 1

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
x1=2x_{1} = 2
x2=1x_{2} = 1
The graph
-12.5-10.0-7.5-5.0-2.50.02.55.07.510.012.515.017.5-50005000
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
1 + 2
1+21 + 2 
=
3
33 
product
2
22 
=
2
22 
2
Rapid solution [src] 
x1 = 1
x1=1x_{1} = 1 
x2 = 2
x2=2x_{2} = 2 
x2 = 2
Numerical answer [src] 
x1 = 1.0
x2 = 2.0
x2 = 2.0
The graph
x+2/x=3 equation
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