(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

y^4 + 3y^2 - 4 = 0

2. Relevant equations

3. The attempt at a solution

The base, I know, is y^2. So in order to make this a quadratic equation, we come up with an arbitrary variable, say α, which is equal to the base. Re-writing this, we get:

(y^2)^2 + 3(y^2) - 4 = 0

α = y^2

α^2 + 3α - 4 = 0

So now it's a quadratic equation.

Factoring, we get:

(α - 1) (α + 4) = 0

Setting both of these equal to zero, we get:

α = 1 and α = -4

This next part is where I'm lost, so maybe one of you bright people can show me where I'm making my mistake.

We start with α = -4.

Since α = y^2, -4 must = y^2 too.

-4 = y^2

Solving this for y, we get:

y = sqrt(-4) = 2i.

However, in the text - without any explanation as to how this occurs (which is what is confusing me about these problems) - it says that the two solutions are 2i and -2i.

Can someone please explain this step to me. D:

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# Homework Help: Equations Quadratic in Form ;_;

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