If [math]\alpha[/math] and [math]\beta[/math] are roots of equation [math]x^2-2px+2p^4[/math], then what is the maximum value of [math]\alpha^2+\beta^2[/math]?
If [math]\alpha[/math] and [math]\beta[/math] are the roots of the equation [math]x^2 -p(x+1)-q=0[/math] then the value of [math]\frac{\alpha^2+2\alpha+1}{\alpha^2+2\alpha+q} + \frac{\beta^2+2\beta+1}{\beta^2+2\beta+q}[/math] is a) 1, B) 2, c) 3, d) 0?