The cubic equation $x^3−2x^2−3x+4=0$ has the roots $α$ , $β$ and $γ$. Using the substitution method how do I find an equation with the roots $ \frac{1}{(α+β)^2}$, $ \frac{1}{(α+γ)^2}$ , $ \frac{1}{(β+γ)^2}$ .
I tried doing it with $\sigma_1$ , $\sigma_2$ and $\sigma_3$ where
$\sigma_1$ is ($\alpha + \beta + \gamma$) ,
$\sigma_2$ is ($\alpha\beta + \alpha\gamma + \beta\gamma)$ and
$\sigma_3$ is ($\alpha\beta\gamma$)
But it is a lengthy method and I guess it will be easier to use the substitutuion method .
Hint $$\alpha + \beta +\gamma =2 \implies \alpha + \beta =2-\gamma $$
So all you need to do is, substitute $$y= \frac1{(2-x)^2}$$