1. ## Homework help

If tanα, tanβ and tanγ are the roots of x^3-(a+1)x^2+(c-a)x-c=0, show that α+β+γ=pi/4.

2. ## Re: Homework help

One approach is to express $\tan(\alpha+\beta+\gamma)$ in terms of $\tan\alpha$, $\tan\beta$ and $\tan\gamma$ by using the angle sum formula twice.

You can show that

$\tan(\alpha+\beta+\gamma) = \frac{\tan\alpha+\tan\beta+\tan\gamma-\tan\alpha\tan\beta\tan\gamma}{1-(\tan\alpha\tan\beta + \tan\alpha\tan\gamma+\tan\beta\tan\gamma)}$

Then find the sum of roots, sum of roots two at a time and product of roots and substitute in.

3. ## Re: Homework help

Originally Posted by fan96
One approach is to express $\tan(\alpha+\beta+\gamma)$ in terms of $\tan\alpha$, $\tan\beta$ and $\tan\gamma$ by using the angle sum formula twice.

You can show that

$\tan(\alpha+\beta+\gamma) = \frac{\tan\alpha+\tan\beta+\tan\gamma-\tan\alpha\tan\beta\tan\gamma}{1-(\tan\alpha\tan\beta + \tan\alpha\tan\gamma+\tan\beta\tan\gamma)}$

Then find the sum of roots, sum of roots two at a time and product of roots and substitute in.
Thx so much!! ^^

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