Respuesta :
The solution of the equation is x=±i or x=±i√2.
Given that the equation is x⁴+3x²+2=0 and use u substitution method to solve.
We can rewrite our given equation as:
(x²)²+3x²+2=0
Let's assume that the (x²)=u.
The given equation is rewritten as u²+3u+2=0.
Factorize the quadratic equation by adding or subtracting two number that gives the sum of 3u and product 2u² as
u²+2u+u+2=0
u(u+2)+1(u+2)=0
Taking out (u+2) as common and get
(u+2)(u+1)=0
Compare each equation with 0 and get
u+2=0 or u+1=0
u=-2 or u=-1
Performing back substitution by substituting the values of u in x²
when u=-1 then x is
x²=-1
x=±√(-1)
As we know that √(-1)=i.
So, we get
x=±i
And when u=-2 then x is
x²=-2
x=±√(-2)
As we know that √(-1)=i.
So, substituting this, we get
x=±i√2
Hence, the solutions of the x⁴+3x²+2=0 is x=±i and x=±i√2.
Learn about the substitution here brainly.com/question/12802700
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