this is a "power series" equation!

TL;DR

Learn how to solve equations with power series using the real way and non-real way, with the non-real way involving the use of complex numbers.

Transcript

hello we are back and today we are going to solve this equation and notice that here we actually have a power series and in fact this equation has infinitely many answers but it's ok because we're just going to find the biggest one and as always please pause the video and try it first and she'll try it to have a look you got it alright so now here ... Read More

Key Insights

• 💨 Equations with power series can be solved using both the real way and the non-real way.
• 💨 The real way involves finding a function that has the desired power series and solving the equation regularly.
• 💨 The non-real way involves using the hyperbolic cosine function, complex numbers, and the natural logarithm to solve the equation.
• ✊ Adjusting the powers in the power series can be done by using the square root of x.
• ☺️ Plugging in negative x in the power series for cosine helps adjust the signs of the terms.
• 💨 The non-real way can be used to solve equations with complex solutions.
• 😒 The real way does not involve the use of complex numbers.

Questions & Answers

Q: What is the difference between the real way and the non-real way of solving equations with power series?

The real way involves finding a function with the desired power series and solving the equation normally, while the non-real way involves using the hyperbolic cosine function and complex numbers to solve the equation.

Q: How do you adjust the powers in the power series to match the desired powers in the equation?

By using the square root of x, you can divide the powers by 2, which allows you to adjust the powers in the power series.

Q: Why do we plug in negative x in the power series for cosine?

Plugging in negative x in the power series for cosine helps adjust the alternating signs of the terms, making them all positive.

Q: How do you solve equations with the hyperbolic cosine function?

To solve equations with the hyperbolic cosine function, you need to use complex numbers and take the natural logarithm to obtain the principal value.

Summary & Key Takeaways

• The content discusses how to solve equations with power series using both the real way and the non-real way.

• The real way involves finding the function with the desired power series and then solving the equation normally.

• The non-real way involves using the hyperbolic cosine function and complex numbers to solve the equation.