I'm in a doubt on the follow equation:
Considering the equation: $x^2 + 5x - 1 = 0$, let $\alpha$ and $\beta$ be solutions; thus $\alpha*\beta = -1$ and $\alpha + \beta = -5$
Evaluate: $\dfrac{1}{\alpha^2} + \dfrac{1}{\beta^2}$
So, working on it, I figured out that the LCM of this fraction would be $\alpha^2*\beta^2$ am I right ?
So working on it, I got:
$\dfrac{\beta^2 + \alpha^2}{\alpha^2*\beta^2}$
Is that right ? and how can I continue to evaluate it ? Thanks in advance;
Edit after @dot dot post:
So, now I've got;
$\dfrac{(\alpha + \beta)^2 - 2*\alpha*\beta}{\alpha^2*\beta^2}$
I'm done with the numerator, but what I have to do with the denominator ?
Is that possible?: $\alpha^2*\beta^2 = (\alpha*\beta)^2$ I think it's not because $2^2*3^2 \neq (2*3)^2$ What should I do now with the denominator ?