Algebra 4th power weirdness problem

Since the equation is of degree 4, there are a maximum of four roots, and they are +/-1, +/-2, +/-3, +/-4, +/-6, +/-8, +/-12, +/-16, +/-24, +/-48. Plugging each of these into the equation, we see that x = 2 is indeed a solution. Therefore, x = 2 is one of the roots of the equation, and the other three roots can be found by dividing the original equation by (x - 2) and solving the resulting cubic equation. In summary, the solution to the equation 4x - x^4/8 = 6 is x = 2, and the other three roots can be found by solving the
  • #1
sarah22
26
0
How did he get x = 2 with this equation? 4x - x^4/8 = 6

Here's my solution:
32x - x^4 - 48
x( x^3 - 32 ) + 48 <---- Now I'm lost. Did he use this one? (a-b)(a^2+ab+b^2) . I tried it but can't think on what to extract.

http://www.wolframalpha.com/input/?i=4x-x^4%2F8%3D6
 
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  • #2
First off, this is an equation: 4x - x^4/8 = 6
This is NOT an equation: 32x - x^4 - 48 -- An equation has an = sign.

The equation is 32x - x^4 - 48 = 0, or equivalently x^4 - 32x + 48 = 0.
This equation can be factored into (x - 2)(x^3 + 2x^2 + 4x -24) = 0.
 
  • #3
"He" would have probably used the rational roots theorem first, if not given any more information.
 

FAQ: Algebra 4th power weirdness problem

What is the "Algebra 4th power weirdness problem"?

The "Algebra 4th power weirdness problem" refers to a mathematical equation that involves taking the fourth power of a variable. This can lead to unexpected and unusual results, which can be confusing for students studying algebra.

How does the "Algebra 4th power weirdness problem" differ from other algebraic equations?

The main difference is that the "Algebra 4th power weirdness problem" involves raising a variable to the fourth power, which can produce more complex and unpredictable solutions compared to equations with lower powers.

Why is the "Algebra 4th power weirdness problem" considered a challenge in algebra?

This problem can be challenging because it requires a strong understanding of algebraic concepts and properties, as well as the ability to handle and manipulate higher powers of variables.

Can you give an example of the "Algebra 4th power weirdness problem"?

Sure, an example could be the equation x^4 = 16. In this case, the solution is not as straightforward as finding the square root of both sides, and some additional steps and techniques may be needed to solve for x.

How can one overcome the "Algebra 4th power weirdness problem"?

The best way to overcome this problem is to practice and understand the fundamental principles of algebra, such as the properties of exponents and how to manipulate equations with higher powers. Also, using examples and working through problems can help develop a better understanding of how to approach and solve these types of equations.

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