SOLUTION: solve y^4-4y^2+4=0(hint: set x=y^2 solve for x, then solve for y after finding x) this makes no sense to me, i feel like it isn't a problem i've learned about

Question 187842: solve y^4-4y^2+4=0(hint: set x=y^2 solve for x, then solve for y after finding x)

this makes no sense to me, i feel like it isn't a problem i've learned about
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Let . This means that

Make the proper substitutions

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the solution is

However, we want to solve for "y"

Go back to the second equation.

Plug in

Rearrange the equation

or Take the square root of both sides (don't forget the "plus/minus")

So the solutions are or
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
solve y^4-4y^2+4=0(hint: set x=y^2 solve for x, then solve for y after finding x)
------------------
Sub x for y^2
x^2 - 4x + 4 = 0
(x-2)*(x-2) = 0
x = 2
------
y^2 = 2
y = +sqrt(2)
y = -sqrt(2)

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