# Extreme Algebra Question (#patience) | Summary and Q&A

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April 7, 2019
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blackpenredpen
Extreme Algebra Question (#patience)

## TL;DR

Solve an extreme algebra question involving the fifth power using multiple equations and identities.

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### 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.