Disequazioni letterali intere es 1-2

[stefano166]

x(x-a) =1-(x^2)

[ce8c0e31f941cc14ed8def9a9c5c3a60a8400d85]

1.

[math]
\begin{aligned}
& x\,(x - a) \le 2\,(a - x) \\
& x\,(x - a) \le - 2\,(x - a) \\
& x\,(x - a) + 2\,(x - a) \le 0 \\
& (x + 2)(x - a) \le 0 \\
& \text{se} \; a < - 2 : a \le x \le - 2 \; ; \\
& \text{se} \; a = - 2 : x = - 2 \; ; \\
& \text{se} \; a > - 2 : - 2 \le x \le a \; .
\end{aligned} \\
[/math]

2.

[math]
\begin{aligned}
& 3\,x^2 + a\,(1 - 2\,x) \ge 1 - x^2 \\
& 4\,x^2 - 1 + a\,(1 - 2\,x) \ge 0 \\
& (2\,x + 1)(2\,x - 1) - a\,(2x - 1) \ge 0 \\
& (2\,x - 1)(2\,x + 1 - a) \ge 0 \\
& \text{se} \; a < 2 : x \le \frac{a - 1}{2} \, \vee \, x \ge \frac{1}{2} \; ; \\
& \text{se} \; a = 2 : \forall\,x \in \mathbb{R} \; ; \\
& \text{se} \; a > 2 : x \le \frac{1}{2} \, \vee \, x \ge \frac{a - 1}{2} \; .
\end{aligned} \\
[/math]

Spero sia sufficientemente chiaro. ;)