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What are the solutions of the equation x^4+3x^2+2=0

User TFS
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ANSWER


x = \pm \: √(2) i \: \: or \: \: x = \pm i

Step-by-step explanation

The given equation is

{x}^(4) + 3 {x}^(2) + 2 = 0


We can rewrite this in the form,


( {x}^(2) ) ^(2) + 3 {x}^(2) + 2 = 0


We can think of this as a quadratic equation in

{x}^(2)


We split the middle term with 2 and 1 to obtain,



( {x}^(2) ) ^(2) + {x}^(2) + 2{x}^(2) + 2 = 0


We factor to obtain,




{x}^(2) ( {x}^(2) + 1) + 2( {x}^(2) + 1) = 0



({x}^(2) + 2)( {x}^(2) + 1) = 0





{x}^(2) = - 2 \: \: or \: \: {x}^(2) = - 1




x = \pm \: √(2) i \: \: or \: \: x = \pm i
User Sergej Panic
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