1 Answer

Sergej Panic · Answer 1 · 2019-11-20T09:56:48+0000

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,

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

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

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

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

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