Extreme Algebra Question (#patience)  Summary and Q&A
TL;DR
Solve an extreme algebra question involving the fifth power using multiple equations and identities.
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.