128. Knowing that $x+\frac{1}{x}=4$, calculate $x^{2}+\frac{1}{x^{2}}$.
$\triangle$ It seems that the equation $x+\frac{1}{x}=4$ should be transformed into a quadratic equation, find $x$ from the quadratic equation, and substitute the obtained value of $x$ into the sum $x^{2}+\frac{1}{x^{2}}$. However, this path is long, especially since the quadratic equation has two roots.

It is simpler to square the original equation:

$$
x^{2}+2+\frac{1}{x^{2}}=16, \quad x^{2}+\frac{1}{x^{2}}=14
$$

Answer: 14.