High School

We appreciate your visit to solve for x x 4 4x 2 21 0. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

solve for x, x^4-4x^2-21=0

Answer :

Final answer:

To solve the equation x^4 - 4x^2 - 21 = 0, we can use the quadratic formula. By substituting x^2 with a new variable, we can simplify the equation and solve for the variable. The solutions to the equation are x = √7 and x = -√7.

Explanation:

To solve the equation x^4 - 4x^2 - 21 = 0, we can use a substitution. Let's substitute x^2 with a new variable, let's say y. The equation becomes y^2 - 4y - 21 = 0. Now we have a new quadratic equation that we can solve using factoring, completing the square, or the quadratic formula.

Let's solve it using the quadratic formula: y = (-(-4) ± √((-4)^2 - 4(1)(-21))) / (2(1)). Simplifying the equation gives us y = (4 ± √(16 + 84)) / 2, which further simplifies to y = (4 ± √100) / 2. Taking the square root of 100 gives us y = (4 ± 10) / 2, which gives us two possible solutions y = 7 and y = -3.

Since y was our substitution for x^2, we substitute back: x^2 = 7 and x^2 = -3. However, x^2 can't be a negative number, so we discard x^2 = -3. Solving x^2 = 7, we take the square root of both sides and get x = ±√7. Therefore, the solutions to the equation x^4 - 4x^2 - 21 = 0 are x = √7 and x = -√7.

Learn more about quadratic equation here:

https://brainly.com/question/30766352

#SPJ1

Thanks for taking the time to read solve for x x 4 4x 2 21 0. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada