How to Solve an Extreme Algebra Question Involving Fifth Powers

TL;DR

To solve the algebra question involving fifth powers, use the equations a+b+c=1, a^2+b^2+c^2=2, and a^3+b^3+c^3=3. Following simplifications and applying identities, the result for a^5+b^5+c^5 is determined to be 6.

Transcript

okay let's do an extreme algebra question for fun  here's the question if a+b+c=1 and a^2+b^2+c^2=2   and a^3+b^3+c^3=3 then let me ask you guys what's  the value for a and we know the fourth power is   going to be too easy so let's deal with the fifth  power let me ask you a^5+b^5+c^5=? and as always   please pause the video and try this first oka... Read More

Key Insights

• ⁉️ The given extreme algebra question involves solving equations with multiple variables and exponents.
• ❓ Trinomial expansion can be used to calculate the expansion of (a+b+c)^n.
• 🧑‍🏭 The solution involves multiplying and factoring terms to simplify the equation.
• ⏮️ The final answer for a^5 + b^5 + c^5 is derived using the values of a, b, and c obtained from previous equations.

Questions & Answers

Q: What is the initial question given in the content?

The initial question is to find the value of a when a+b+c=1, a^2+b^2+c^2=2, and a^3+b^3+c^3=3.

Q: How is the value of a calculated in the given equations?

One approach is to multiply the first and second equations together to get a^2 + b^2 + c^2 = 2ab + 2ac + 2bc. Then, substitute the values in the third equation to solve for a.

Q: How does the content explain the concept of trinomial expansion?

The content explains the concept of trinomial expansion, where the expansion of (a+b+c)^n can be calculated using trinomial coefficients and multiple indexes.

Q: How is the calculation of a^5 + b^5 + c^5 done using the given equations?

By expanding and simplifying the equation, a^5 + b^5 + c^5 is calculated as 2(a^2b + a^2c + b^2a + b^2c + c^2a + c^2b) + 6abc.

Summary & Key Takeaways

• The question involves solving an algebraic equation with multiple variables and exponents.

• By using various equations and identities, the value of a, b, and c is determined.

• The equation is then expanded and simplified to calculate the value of a^5 + b^5 + c^5.