What Went Wrong? Solving for X in an Inequality

  • Thread starter jrdunaway
  • Start date
In summary, the conversation was about solving for x in the inequality x^2 + x + 1 > 2. The attempt at a solution involved a mistake in factorizing the quadratic, not considering the possibility of negative solutions, and incorrectly expressing the solution as x > 2, x > 1/2. The correct methods to solve the inequality are finding the discriminant and completing the square.
  • #1
jrdunaway
3
0

Homework Statement



Solve for X

Homework Equations



x^2 + x + 1 > 2

The Attempt at a Solution



x2 + x - 1 > 0

(x + 2)(x - 1/2) > 0

x > 2
x > 1/2

Wolfram Alpha said that the solutions for X are:

x>1/2 (sqrt(5)-1)

and

x<1/2 (-1-sqrt(5))

what did I do wrong?
 
Last edited:
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  • #2
jrdunaway said:

Homework Statement



Solve for X

Homework Equations



x^2 + x + 1 > 2

The Attempt at a Solution



x2 + x - 1 > 0

(x + 2)(x - 1/2) > 0

x > 2
x > 1/2

Wolfram Alpha said that the solutions for X are:

x>1/2 (sqrt(5)-1)

and

x<1/2 (-1-sqrt(5))

what did I do wrong?

Well, for one thing, your factorisation of x2 + x - 1 to (x + 2)(x - 1/2) is wrong.

You can see that by multiplying those factors together. They won't equal the original quadratic.

What's the discriminant of the quadratic?

The other error is in supposing that, if AB > 0, then A > 0 and B > 0 is the only solution. Don't forget that A < 0 and B < 0 is also a valid solution. Remember, if you multiply two negative numbers together, you get a positive.

Another mistake was going from x + 2 > 0 to x > 2. Shouldn't that be x > -2?

The last mistake was in the way you expressed your solution. Even though you considered the A > 0 and B > 0 case, you wrote the solution as x > 2, x > 1/2. Remember the "AND" condition. If x > 2 AND x > 1/2, you should simply "collapse" that solution to x > 2 (the bigger value) since everything that's bigger than 2 is also bigger than 1/2. Of course, 2 and 1/2 are wrong values for this question (as I mentioned earlier), but I'm using them to demonstrate the concept for you.
 
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  • #3
jrdunaway said:
what did I do wrong?

Here is what you did wrong:
x2 + x - 1 > 0

(x + 2)(x - 1/2) > 0

(x+2)(x-1/2) = x2 + 1.5x - 1, not x2 + x - 1.
 
  • #4
Why would you go trying to factor when all you have to do is bring the 2 to the left side and solve the equation (x^2+x+?=0) by finding the discriminant Δ and you'll get 2 real roots. Then go on from there.
 
  • #5
Another method is to complete the square, getting p^2 > ...
 

1. What is the purpose of "Solving X: What Went Wrong?"

The purpose of "Solving X: What Went Wrong?" is to identify and address a problem or failure in a systematic and scientific manner. By analyzing the root causes and underlying factors, this process aims to find solutions and prevent similar issues from occurring in the future.

2. How do you determine what went wrong?

To determine what went wrong, scientists use various methods such as data analysis, experiments, and observations. They also rely on established theories and laws to guide their investigations. It is crucial to objectively examine all evidence and consider various perspectives to accurately identify the problem.

3. What are the benefits of using a scientific approach to solve a problem?

Using a scientific approach to solve a problem offers several benefits, including a systematic and organized way of thinking, the use of evidence-based solutions, and the ability to replicate and verify results. This approach also encourages critical thinking and open-mindedness, leading to more effective and efficient problem-solving.

4. What are some common mistakes or challenges in the problem-solving process?

Some common mistakes or challenges in the problem-solving process include biases, lack of relevant data or information, and overlooking important factors. It is also essential to consider the limitations of the scientific method and be open to revising theories and solutions as new evidence emerges.

5. How can we apply the lessons learned from "Solving X: What Went Wrong?" to future situations?

The lessons learned from "Solving X: What Went Wrong?" can be applied to future situations by developing strategies and protocols to prevent similar problems, continuously monitoring and evaluating processes, and incorporating feedback and new information into decision-making. It is also crucial to promote a culture of learning and improvement, where mistakes are seen as opportunities for growth and progress.

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