sum and product of roots of polynomials: finding equations for roots

Question

this question pertains to the sum and product of roots.

$x^2 + 2x + 5 = 0$ has roots $\alpha$ and $\beta$, hence $\alpha + \beta = 2$ and
$\alpha \beta = 5$.

Find the equation which has roots $\alpha^2$ and $\beta^2$ using the method $x=\alpha$ or $x=\beta$, and $u = \alpha^2$ or $u = \beta^2$, then $\alpha = \sqrt u$ or $\beta = \sqrt u$

I can solve it by $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha \beta$ etc... but not using the other method above. what's the technique here?

Answer 1

Hint

Note that $x^2 + 2x + 1 = (x+1)^2$.

What substitution do you use?