Prove x^4 + 6x^2 - 1 = 0 has exactly two solutions.

Question:

Prove {eq}x^4 + 6x^2 - 1 = 0 {/eq} has exactly two solutions.

Solution of Equation:

We have to prove that the given equation has exactly two solutions. First we will substitute {eq}u=x^2 {/eq} into the given equation. We will use quadratic formula to find the solution of the given equation to get the desired result.

Answer and Explanation:

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Using the quadratic formula we have $$\begin{align*} {x^4} + 6{x^2} - 1 &= 0{\text{ substitute }}u = {x^2}\\ {u^2} + 6u - 1 &= 0\\ u &=...

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The Quadratic Formula: Definition & Example

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Chapter 25 / Lesson 10
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Watch this video lesson to learn how you can use the quadratic formula to solve certain types of problems. Learn what kinds of equations you can solve using this formula as well as how easy it is to use this formula.


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