SOLUTION: x^-4-3x^-2-4=0

Question 186689: x^-4-3x^-2-4=0
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Let . So this means that

Replace with . Replace with

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

Let's use the quadratic formula to solve for z

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

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Start with the first solution

Plug in

Rewrite the left side with a positive exponent.

Multiply both sides by .

Divide both sides by 4 and rearrange the equation

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

or Take the square root of to get

So the first two solutions are or

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Start with the second solution

Plug in

Rewrite the left side with a positive exponent.

Multiply both sides by

Divide both sides by -1 and rearrange the equation.

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

or Simplify (note:

So the next two solutions are or

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Answer:

So the solutions are , , or
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