Can someone solve this equation for a?

Thread starter Icebreaker
Start date Apr 28, 2005

AI Thread Summary

To solve the equation b²a + 2bc² = (a³b²/c²) + 2ba² + c²a, the goal is to find the value of 'a' such that P(a) = 0, where P(x) is defined as (b/c)²x³ + (2b)x² + (c² - b²)x - 2bc². Factoring the cubic polynomial P will yield a form of P(x) = (x - a)(dx² + ex + f), allowing for the identification of the desired value of 'a'. The discussion emphasizes the importance of understanding how to factor cubic equations to find the roots. Ultimately, the solution hinges on successfully factoring the cubic polynomial.

Apr 28, 2005

Icebreaker

Can someone solve this equation for a?

b^2a+2bc^2=\frac{a^3b^2}{c^2}+2ba^2+c^2a

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Apr 28, 2005

AKG

Science Advisor

Homework Helper

P(x) = (b/c)²x³ + (2b)x² + (c² - b²)x + (-2bc²)

We want to find a such that P(a) = 0

Factor this cubic P, and you'll get something in the form P(x) = (x - a)(dx² + ex + f)

That a is precisely the one you're looking for. How to factor cubics.

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