How do you solve 8y^4 - 4y^2 = 0?

3 Answers
Jul 30, 2016

y= 0" , " y=+-sqrt(2)/2

Explanation:

Factor out y^2 giving:" "y^2(8y^2-4)=0

So y^2=0=>y=0

Or color(brown)((8y^2-4)=0)color(green)(" " =>" " y^2=1/2)color(purple)(" " =>" " y=+-1/sqrt(2)=+-sqrt(2)/2)

Jul 30, 2016

y = 0 or y = +-sqrt(1/2)

Explanation:

Find the factors first., look for a common factor before doing anything else.

8y^4 - 4y^2 = 0

4y^2(2y^2 - 1)= 0

Either of the factors could be equal to 0.
Make two equations and solve each.

if 4y^2 = 0" "rArr y^2 = 0 " "rArr y = 0

if 2y^2 - 1 =0 " "rArr2y^2 = 1" "rArr y^2 = 1/2

y = 0 or y = +-sqrt(1/2)

Jul 30, 2016

y=-sqrt2/2," "0," "sqrt2/2

Explanation:

First, notice that both terms have a common factor of 4y^2. This can be factored out of both terms.

8y^4-4y^2=0

4y^2((8y^4)/(4y^2)-(4y^2)/(4y^2))=0

4y^2(2y^2-1)=0

We now have two different terms being multiplied to equal 0. The first is just 4y^2, and the other is the entirety of (2y^2-1).

We can use the "Zero Factor Property" here, which basically states that if factors are being multiplied to equal 0, it stands to reason that either factor must also equal 0. (If ab=0, then either a=0 or b=0.)

So here, we know that:

{(4y^2=0),(2y^2-1=0):}

Solving the first:

4y^2=0

This boils down to our first solution:

barul|color(white)(a/a)y=0color(white)(a/a)|

Solving the second:

2y^2-1=0

2y^2=1

y^2=1/2

Taking the square root of both sides (remember to allow positive and negative solutions):

y=+-sqrt(1/2)=+-1/sqrt2=+-sqrt2/2

Giving 2 more solutions:

barul|color(white)(a/a)y=sqrt2/2color(white)(a/a)|

barul|color(white)(a/a)y=-sqrt2/2color(white)(a/a)|