Simple Problem STUMPS PhotoMath! Can You Figure It Out?
TLDRIn this Mind Your Decisions video, Presh Talwalkar tackles an algebra problem that stumps PhotoMath and other solvers, challenging viewers to solve for x in the equation \(x^2 - 7x + 11\) raised to the power of \(x^2 - 13x + 42\) equals 1. The video reveals that while solvers like PhotoMath and Mathway find four solutions, there are actually six, including cases where the base is 1, the exponent is 0, and negative one raised to an even power. The solutions are x = 2, 3, 4, 5, 6, and 7, with a humorous note on multiplying these solutions.
Takeaways
- 🧠 The problem involves solving the equation (x^2 - 7x + 11) raised to the power of (x^2 - 13x + 42) equals 1 for all real numbers x.
- 📱 Popular math-solving apps like Photomath, Mathway, and Symbolab struggle with this problem, missing some solutions.
- 📊 Desmos graphing calculator suggests four solutions, but there are actually six.
- 🔍 Wolfram Alpha is the only solver mentioned that finds all six solutions.
- 📝 The first case to consider is where the base equals 1, leading to the factorization of (x^2 - 7x + 11) and solutions x = 2 and x = 5.
- 📉 The second case is where the exponent equals 0, resulting in the factorization of (x^2 - 13x + 42) and solutions x = 6 and x = 7.
- ❌ It's important to check that the base is not zero to avoid the indeterminate form of 0 to the power of 0.
- 🔄 The third case involves the base being -1, which is true when the exponent is even, leading to solutions x = 3 and x = 4 after factoring.
- 🤔 The video challenges viewers to find the product of all solutions as a joke, hinting at a humorous or unexpected result.
- 🎓 The video serves as an educational resource, aiming to inspire and build confidence in math for viewers worldwide.
Q & A
What is the main problem presented in the video?
-The main problem in the video is to solve for all real numbers x for which the expression \((x^2 - 7x + 11)^{(x^2 - 13x + 42)}\) equals 1.
Why is the problem challenging for computer solvers like PhotoMath?
-The problem is challenging for computer solvers because they often miss some solutions. PhotoMath, for example, suggests there are four solutions, but there are actually six.
How many solutions does the presenter claim the problem has?
-The presenter claims that the problem has six solutions.
What is the first case the presenter considers to solve the problem?
-The first case the presenter considers is when the base of the exponent is 1, which leads to the equation \(x^2 - 7x + 11 = 1\).
What are the solutions obtained from the first case?
-From the first case, the solutions obtained are \(x = 2\) and \(x = 5\).
What is the second case considered in the video?
-The second case considered is when the exponent is 0, which leads to the equation \(x^2 - 13x + 42 = 0\).
What are the solutions from the second case?
-The solutions from the second case are \(x = 6\) and \(x = 7\).
Why is it important to check that the base is not zero?
-It is important to check that the base is not zero because \(0^0\) is an indeterminate form, and it does not provide a meaningful solution.
What is the third case explored in the video?
-The third case explored is when the base is -1 and the exponent is an even number, leading to the equation \(x^2 - 7x + 11 = -1\).
What are the solutions from the third case?
-The solutions from the third case are \(x = 3\) and \(x = 4\), but only when the exponent is even, which happens when \(x = 3\) and \(x = 4\).
Which solver is mentioned as being able to find all six solutions?
-Wolfram Alpha is mentioned as the solver that is able to find all six solutions.
What joke does the presenter leave the viewers with?
-The joke left for the viewers is to multiply all the solutions together and read out the sentence: 'Did you figure it out?'
Outlines
🧠 Challenging Algebra Problem
Presh Talwalkar introduces a complex algebra problem involving solving for real numbers x where an expression involving x squared, subtracted by 7x plus 11, raised to the power of another expression, equals 1. The problem is reminiscent of those given to Massachusetts high school students, with an average solving time of 30 minutes per question. The video challenges viewers to solve it before revealing the solution. Many students rely on apps and websites for step-by-step solutions, but for this problem, popular solvers like Photomath, Mathway, and Symbolab fail to provide all correct solutions, missing two out of six possible solutions. Only Wolfram Alpha correctly identifies all six solutions. The video emphasizes the importance of solving problems independently and checking solutions provided by solvers.
Mindmap
Keywords
💡Algebra
💡Exponents
💡Polynomial
💡Solving Equations
💡Factoring
💡Zero Exponent Rule
💡Indeterminate Form
💡Negative One Raised to an Even Power
💡Wolfram Alpha
💡Photomath
Highlights
Presh Talwalkar presents a challenging algebra problem involving exponents and quadratic equations.
The problem requires solving for x in the equation (x^2 - 7x + 11)^(x^2 - 13x + 42) = 1.
High school students in Massachusetts were given an average of 30 minutes to solve similar problems.
Many computer solvers, including Photomath, fail to find all solutions for this problem.
Wolfram Alpha is noted for finding all six solutions, unlike other solvers that miss some.
The first case to consider is when the base of the exponent is 1, leading to a factored equation (x - 2)(x - 5) = 0.
Setting the exponent to zero gives another case, resulting in the solutions x = 6 and x = 7.
It's important to check that the base is not zero to avoid an indeterminate form.
The third case involves the base being -1, which requires the exponent to be even.
Solving for the base equal to -1 yields two potential solutions: x = 3 and x = 4.
The exponent must be checked to ensure it is even, confirming x = 3 and x = 4 as valid solutions.
The video concludes with all six solutions: x = 2, 3, 4, 5, 6, and 7.
A joke is shared about multiplying all the solutions together.
The video encourages viewers to subscribe for more free math content on YouTube.
Presh invites viewers to email him with puzzles or math topics for future videos.
Merchandise and books related to the channel are mentioned for those interested.
Support for the channel is available through Patreon for exclusive rewards.