Equation I simply don't understand I am working on some math problems from math books, and I have seen this in one math problem.
$x_1^2+x_2^2= (x_1+x_2)^2 - 2x_1x_2$
I simply don't understand this. Can you please explain this to me.  
The whole math problem is:
You have this equation
$x^2 - 3x + m^2 -1 = 0$
For what parameter m is:
$x_1^2 + x_2^2 > 3$

I think what's going on is that you want to find all values of the constant $m$ so that, if $x_1$ and $x_2$ are the two (not necessarily distinct) solutions to the equation $x^2 - 3x + m^2 -1 = 0,$ then $x_{1}^{2} + x_{2}^{2} > 3.$
Recall Vieta's formulas for the sum and product of the solutions of the quadratic equation $ax^2 + bx + c = 0.$ They say that the sum of the solutions equals $-\frac{b}{a}$ and the product of the solutions equals $\frac{c}{a}.$
Thus, in the case of your quadratic equation, we have $x_{1} + x_{2} = 3$ and $x_{1}x_{2}=m^2 - 1.$ Since $x_{1}^{2} + x_{2}^{2} = \left(x_1 + x_2\right)^2 - 2x_{1}x_{2},$ it follows that $x_{1}^{2} + x_{2}^{2} = 3^2 - 2(m^2 - 1) = 11 - 2m^2.$ Therefore, $x_{1}^{2} + x_{2}^{2} > 3$ becomes $11 - 2m^2 > 3,$ or $m^2 < 4,$ or $-2 < m < 2.$
