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Solving inequalities/ x^2+1

x^2+1 inequation

A inequation with variable

The solution

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 2        
x  + 1 > 0
x2+1>0x^{2} + 1 > 0 
x^2 + 1 > 0
Detail solution
Given the inequality:
x2+1>0x^{2} + 1 > 0
To solve this inequality, we must first solve the corresponding equation:
x2+1=0x^{2} + 1 = 0
Solve:
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=0b = 0
c=1c = 1
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (1) = -4

Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)

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

or
x1=ix_{1} = i
x2=−ix_{2} = - i
x1=ix_{1} = i
x2=−ix_{2} = - i
Exclude the complex solutions:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
x0 = 0

02+1>00^{2} + 1 > 0
1 > 0

so the inequality is always executed
Solving inequality on a graph
-5.0-4.0-3.0-2.0-1.05.00.01.02.03.04.0020
Rapid solution
This inequality holds true always
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