SOLUTION: For the following, solve. Find exact solutions {{{y^4-3y^2=-1}}}

Question 142982: For the following, solve. Find exact solutions

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Add 1 to both sides

Let . So this means that

Replace with . Replace with .

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=-3, and c=1

Negate -3 to get 3

Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

So the solutions in terms of x are

or

But remember, we let . So this means

or

Take the square root of both sides in each case

or

So after breaking up the expressions, we get the four solutions

, , ,
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