# Solving x^4 - x^2 = k for x: Tips and Tricks to Simplify Equations

• Ted123
In summary, to simplify the equation x^4 - x^2 = k, you can factor out the common term x^2 and use the quadratic formula to solve for x^2 and then take the square root to find the values of x. The first step in solving this equation is to rearrange it to get it in the form x^4 - x^2 - k = 0. Yes, the quadratic formula can be used to solve x^4 - x^2 = k, but you will need to take the square root of both solutions for x^2. Other methods for solving this equation include using the substitution method and checking your solution by plugging it back into the original equation or graphing it.
Ted123
Solve the equation $$x^4 - x^2 = k$$ where $k>0$.

Am I being thick or how do I solve this for $x$?

Factorising gives $$x^2(x^2-1)=k$$ but now where?

Let $y= x^2$ and that becomes a quadratic function:
$y^2- y= k$ or $y^2- y- k= 0$. Solve that for y, then solve $x^2= y$ for x.

## 1. How do I simplify the equation x^4 - x^2 = k?

To simplify this equation, you can rewrite it as x^2(x^2 - 1) = k and then factor out the common term x^2. This will leave you with x^2 = k / (x^2 - 1). You can then use the quadratic formula to solve for x^2 and then take the square root to find the values of x.

## 2. What is the first step in solving x^4 - x^2 = k?

The first step is to rearrange the equation to get it in the form x^4 - x^2 - k = 0. This makes it easier to factor and solve for x.

## 3. Can I use the quadratic formula to solve x^4 - x^2 = k?

Yes, you can use the quadratic formula to solve this equation. However, you will end up with two solutions for x^2, so you will need to take the square root of both solutions to get the values for x.

## 4. Are there any other methods for solving x^4 - x^2 = k?

Yes, you can also use the substitution method by letting y = x^2 and solving for y. Once you have the values of y, you can then substitute them back into the original equation to find the values of x.

## 5. How can I check my solution for x^4 - x^2 = k?

You can check your solution by plugging the values of x back into the original equation and seeing if it equals the given value of k. You can also graph the equation and see if the x-intercepts match your solutions.

• Calculus and Beyond Homework Help
Replies
1
Views
436
• Calculus and Beyond Homework Help
Replies
7
Views
698
• Calculus and Beyond Homework Help
Replies
5
Views
529
• Calculus and Beyond Homework Help
Replies
7
Views
677
• Calculus and Beyond Homework Help
Replies
2
Views
911
• Calculus and Beyond Homework Help
Replies
3
Views
488
• Calculus and Beyond Homework Help
Replies
8
Views
757
• Calculus and Beyond Homework Help
Replies
7
Views
266
• Calculus and Beyond Homework Help
Replies
4
Views
489
• Calculus and Beyond Homework Help
Replies
4
Views
935