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x^4-2x^2+1=0

x^4-2x^2+1=0 equation

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Numerical solution:

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The solution

You have entered [src] 
 4      2        
x  - 2*x  + 1 = 0
x4−2x2+1=0x^{4} - 2 x^{2} + 1 = 0
Simplify
Detail solution
Given the equation:
x4−2x2+1=0x^{4} - 2 x^{2} + 1 = 0
Do replacement
v=x2v = x^{2}
then the equation will be the:
v2−2v+1=0v^{2} - 2 v + 1 = 0
This equation is of the form
a*v^2 + b*v + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
v1=D−b2av_{1} = \frac{\sqrt{D} - b}{2 a}
v2=−D−b2av_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=−2b = -2
c=1c = 1
, then
D = b^2 - 4 * a * c = 

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

Because D = 0, then the equation has one root.
v = -b/2a = --2/2/(1)

v1=1v_{1} = 1
The final answer:
Because
v=x2v = x^{2}
then
x1=v1x_{1} = \sqrt{v_{1}}
x2=−v1x_{2} = - \sqrt{v_{1}}
then:
x1=01+1⋅1121=1x_{1} = \frac{0}{1} + \frac{1 \cdot 1^{\frac{1}{2}}}{1} = 1
x2=(−1)1121+01=−1x_{2} = \frac{\left(-1\right) 1^{\frac{1}{2}}}{1} + \frac{0}{1} = -1
The graph
05-15-10-51015020000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -1
x1=−1x_{1} = -1
Simplify 
x2 = 1
x2=1x_{2} = 1
Simplify
Sum and product of roots [src] 
sum
0 - 1 + 1
(−1+0)+1\left(-1 + 0\right) + 1 
=
0
00 
product
1*-1*1
1(−1)11 \left(-1\right) 1 
=
-1
−1-1 
-1
Numerical answer [src] 
x1 = -1.0
x2 = 1.0
x2 = 1.0
The graph
x^4-2x^2+1=0 equation
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