Question 1045527
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What are the solutions of the equation x4 + 3x2 + 2 = 0? Use u substitution to solve.
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{{{x^4 + 3x^2 + 2}}} = {{{0}}}.


Introduce a new variable u = {{{x^2}}}.

Then your original equation takes the form

{{{u^2 + 3x + 2}}} = {{{0}}}.

Factor the left side:

(u+1)*(u+2) = 0.

The solutions of this equation are


a)  u = -1, which means {{{x^2}}} = -1.  This equation has no real solutions.
            It has two complex solutions  x = i  and  x = -i, where i = {{{sqrt(-1)}}}.


a)  u = -2, which means {{{x^2}}} = -2.  This equation has no real solutions.
            It has two complex solutions  x = {{{sqrt(2)*i}}}  and  x = {{{-sqrt(2)*i}}}.


<U>Answer</U>.  There is no real solutions.
         There are four complex solutions  x = i,  x = -i,  x = {{{sqrt(2)*i}}}  and  x = {{{-sqrt(2)*i}}}
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