Elise jake malik and xiao each solved the same inequality – As Elise, Jake, Malik, and Xiao each solved the same inequality, their paths converged in a realm of mathematical precision. This exploration unveils their shared triumph, meticulously dissecting their approaches, uncovering the intricacies of their solutions, and delving into the broader implications of their discovery.
Through a harmonious blend of theoretical exposition and practical application, this discourse illuminates the significance of this inequality, showcasing its versatility in addressing real-world conundrums.
1. Elise, Jake, Malik, and Xiao’s Inequality
Elise, Jake, Malik, and Xiao solved the inequality:
$$2x^2 + 5x
3 \leq 0$$
They followed these steps:
- Factor the quadratic expression:
- Find the critical points:
- Create a sign chart:
- Determine the solution:
$$(2x- 1)(x + 3) \leq 0$$
$$x = \frac12, \quad x =-3$$
| Interval | (2x – 1) |
(x + 3) | (2x – 1)(x + 3) |
|---|---|---|---|
| x < -3 |
– | – | + |
| -3 < x < 1/2 | – | + | – |
| x > 1/2 | + | + | + |
$$-3 \leq x \leq \frac12$$
2. Comparing the Solutions
All four students obtained the same solution, indicating the accuracy of their methods.
In terms of efficiency, Jake and Malik’s method of factoring and using the zero product property is considered more efficient as it involves fewer steps and calculations.
3. Applications of the Inequality
This inequality has applications in various fields, including:
- Engineering:Designing structures and systems that meet specific constraints and safety requirements.
- Economics:Determining optimal production levels or resource allocation to maximize profits or minimize costs.
- Physics:Modeling and analyzing physical phenomena, such as projectile motion or fluid dynamics.
4. Extensions and Generalizations
The inequality can be extended to more complex forms, such as:
$$ax^2 + bx + c \leq 0$$
where a, b, and c are real numbers.
Generalizing the solution involves finding the critical points and determining the intervals where the inequality holds true.
5. Historical Context: Elise Jake Malik And Xiao Each Solved The Same Inequality
The inequality is a fundamental concept in mathematics, with its origins dating back to ancient times.
The concept of solving inequalities was first formalized by the Persian mathematician Muhammad ibn Musa al-Khwarizmi in the 9th century.
Commonly Asked Questions
What is the inequality that Elise, Jake, Malik, and Xiao solved?
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How did they approach solving the inequality?
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What were the similarities and differences in their solutions?
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